Local BRST cohomology in gauge theories. (English) Zbl 1097.81571
The general solution of the anomaly consistency condition (Wess-Zumino equation) has been found recently for Yang-Mills gauge theory. The general form of the counterterms arising in the renormalization of gauge-invariant operators (Kluberg-Stern and Zuber conjecture) and in gauge theories of the Yang-Mills type with non-power counting renormalizable couplings has also been worked out in any number of space-time dimensions. This Physics Report is devoted to reviewing in a self-contained manner these results and their proofs. This involves computing cohomology groups of the differential introduced by Becchi, Rouet, Stora and Tyutin, with the sources of the BRST variations of the fields (“antifields”) included in the problem. Applications of this computation to other physical questions (classical deformations of the action, conservation laws) are also considered. The general algebraic techniques developed in the Report can be applied to other gauge theories, for which relevant references are given.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T70 | Quantization in field theory; cohomological methods |
References:
| [1] | M. Alexandrov, M. Kontsevich, A. Schwartz, O. Zaboronsky, The geometry of the master equation and topological quantum field theory, Int. J. Mod. Phys. A 12 (1997) 1405 hep-th/9502010.; M. Alexandrov, M. Kontsevich, A. Schwartz, O. Zaboronsky, The geometry of the master equation and topological quantum field theory, Int. J. Mod. Phys. A 12 (1997) 1405 hep-th/9502010. · Zbl 1073.81655 |
| [2] | Alvarez-Gaumé, L.; Witten, E., Gravitational anomalies, Nucl. Phys. B, 234, 269 (1984) |
| [3] | Anco, S. C., New spin-one gauge theory in three dimensions, J. Math. Phys., 36, 6553 (1995) · Zbl 0845.58065 |
| [4] | Anco, S. C., Novel generalization of three-dimensional Yang-Mills theory, J. Math. Phys., 38, 3399 (1997) · Zbl 0893.53031 |
| [5] | Anderson, I. M.; Duchamp, T., On the existence of global variational principles, Am. J. Math., 102, 781 (1980) · Zbl 0454.58021 |
| [6] | Anderson, I. M., Introduction to the variational bicomplex, Contemp. Math., 132, 51 (1992) · Zbl 0772.58013 |
| [7] | Anselmi, D., Removal of divergences with the Batalin-Vilkovisky formalism, Class. Quant. Grav., 11, 2181 (1994) · Zbl 0805.58068 |
| [8] | D. Anselmi, More on the subtraction algorithm, Class. Quant. Grav. 12 (1995) 319 hep-th/9407023.; D. Anselmi, More on the subtraction algorithm, Class. Quant. Grav. 12 (1995) 319 hep-th/9407023. · Zbl 0820.58060 |
| [9] | Arnowitt, R.; Deser, S., Interaction between gauge vector fields, Nucl. Phys., 49, 133 (1963) |
| [10] | B. Geyer, P.M. Lavrov, D. Mülsch, Osp (1, 1)- covariant quantization of reducible massive gauge theories, J. Math. Phys. 40 (1999) 6189, hep-th/9806117.; B. Geyer, P.M. Lavrov, D. Mülsch, Osp (1, 1)- covariant quantization of reducible massive gauge theories, J. Math. Phys. 40 (1999) 6189, hep-th/9806117. |
| [11] | G. Bandelloni, A. Blasi, C. Becchi, R. Collina, Nonsemisimple gauge models: 1, classical theory and the properties of ghost states, Ann. Inst. Henri Poincaré Phys. Theor. \(28 (1978) 225.^*\); G. Bandelloni, A. Blasi, C. Becchi, R. Collina, Nonsemisimple gauge models: 1, classical theory and the properties of ghost states, Ann. Inst. Henri Poincaré Phys. Theor. \(28 (1978) 225.^*\) |
| [12] | G. Bandelloni, A. Blasi, C. Becchi, R. Collina, Nonsemisimple gauge models: 2, renormalization, Ann. Inst. Henri Poincaré Phys. Theor. \(28 (1978) 255.^*\); G. Bandelloni, A. Blasi, C. Becchi, R. Collina, Nonsemisimple gauge models: 2, renormalization, Ann. Inst. Henri Poincaré Phys. Theor. \(28 (1978) 255.^*\) |
| [13] | Bandelloni, G., Yang-Mills cohomology in four-dimensions, J. Math. Phys., 27, 2551 (1986) · Zbl 0599.55005 |
| [14] | Bandelloni, G., Nonpolynomial Yang-Mills Local Cohomology, J. Math. Phys., 28, 2775 (1987) · Zbl 0635.55010 |
| [15] | Bandelloni, G.; Lazzarini, S., Diffeomorphism cohomology in Beltrami parametrization, J. Math. Phys., 34, 5413 (1993) · Zbl 0884.32016 |
| [16] | G. Bandelloni, S. Lazzarini, Diffeomorphism cohomology in Beltrami parametrization. 2: the 1 forms, J. Math. Phys. 36 (1995) 1 (hep-th/9410190).; G. Bandelloni, S. Lazzarini, Diffeomorphism cohomology in Beltrami parametrization. 2: the 1 forms, J. Math. Phys. 36 (1995) 1 (hep-th/9410190). · Zbl 0884.32017 |
| [17] | Bardeen, W. A., Anomalous ward identities in spinor field theories, Phys. Rev., 184, 1848 (1969) |
| [18] | Bardeen, W. A.; Zumino, B., Consistent and covariant anomalies in gauge and gravitational theories, Nucl. Phys. B, 244, 421 (1984) |
| [19] | G. Barnich, M. Henneaux, Consistent couplings between fields with a gauge freedom and deformations of the master equation, Phys. Lett. B 311 (1993) 123 (hep-th/9304057).; G. Barnich, M. Henneaux, Consistent couplings between fields with a gauge freedom and deformations of the master equation, Phys. Lett. B 311 (1993) 123 (hep-th/9304057). |
| [20] | G. Barnich, M. Henneaux, R. Tatar, Consistent interactions between gauge fields and local BRST cohomology: the example of Yang-Mills models, Int. J. Mod. Phys. D 3 (1994) 139 (hep-th/9307155).; G. Barnich, M. Henneaux, R. Tatar, Consistent interactions between gauge fields and local BRST cohomology: the example of Yang-Mills models, Int. J. Mod. Phys. D 3 (1994) 139 (hep-th/9307155). |
| [21] | G. Barnich, M. Henneaux, Renormalization of gauge invariant operators and anomalies in Yang-Mills theory, Phys. Rev. Lett. 72 (1994) 1588 (hep-th/9312206).; G. Barnich, M. Henneaux, Renormalization of gauge invariant operators and anomalies in Yang-Mills theory, Phys. Rev. Lett. 72 (1994) 1588 (hep-th/9312206). · Zbl 0973.81536 |
| [22] | G. Barnich, F. Brandt, M. Henneaux, Conserved currents and gauge invariance in Yang-Mills theory, Phys. Lett. B 346 (1995) 81 (hep-th/9411202).; G. Barnich, F. Brandt, M. Henneaux, Conserved currents and gauge invariance in Yang-Mills theory, Phys. Lett. B 346 (1995) 81 (hep-th/9411202). · Zbl 0925.53044 |
| [23] | G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. I. General theorems, Commun. Math. Phys. 174 (1995) 57 (hep-th/9405109).; G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. I. General theorems, Commun. Math. Phys. 174 (1995) 57 (hep-th/9405109). · Zbl 0844.53059 |
| [24] | G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. II. Application to Yang-Mills theory, Commun. Math. Phys. 174 (1995) 93 (hep-th/9405194).; G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in the antifield formalism. II. Application to Yang-Mills theory, Commun. Math. Phys. 174 (1995) 93 (hep-th/9405194). · Zbl 0844.53060 |
| [25] | G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in Einstein Yang-Mills theory, Nucl. Phys. B 455 (1995) 357 (hep-th/9505173).; G. Barnich, F. Brandt, M. Henneaux, Local BRST cohomology in Einstein Yang-Mills theory, Nucl. Phys. B 455 (1995) 357 (hep-th/9505173). · Zbl 0925.53044 |
| [26] | G. Barnich, M. Henneaux, T. Hurth, K. Skenderis, Cohomological analysis of gauged-fixed gauge theories, (hep-th/9910201) to appear in Phys. Lett. B.; G. Barnich, M. Henneaux, T. Hurth, K. Skenderis, Cohomological analysis of gauged-fixed gauge theories, (hep-th/9910201) to appear in Phys. Lett. B. · Zbl 0976.81119 |
| [27] | I.A. Batalin, G.A. Vilkovisky, Relativistic S matrix of dynamical systems with Boson and fermion constraints, Phys. Lett. 69 B (1977) 309.; I.A. Batalin, G.A. Vilkovisky, Relativistic S matrix of dynamical systems with Boson and fermion constraints, Phys. Lett. 69 B (1977) 309. |
| [28] | Batalin, I. A.; Vilkovisky, G. A., Gauge algebra and quantization, Phys. Lett., 102 B, 27*** (1981) |
| [29] | Batalin, I. A.; Vilkovisky, G. A., Feynman rules for reducible gauge theories, Phys. Lett. B, 120, 166 (1983) |
| [30] | Batalin, I. A.; Vilkovisky, G. A., Quantization of gauge theories with linearly dependent generators, Phys. Rev. D, 28, 2567* (1983) |
| [31] | Batalin, I. A.; Fradkin, E. S., A generalized canonical formalism and quantization of reducible gauge theories, Phys. Lett., 122 B, 157 (1983) · Zbl 0967.81508 |
| [32] | Batalin, I. A.; Vilkovisky, G. A., Closure of the gauge algebra, generalized Lie equations and Feynman rules, Nucl. Phys. B, 234, 106 (1984) |
| [33] | I.A. Batalin, G.A. Vilkovisky, Existence theorem for gauge algebra, J. Math. Phys. \(26 (1985) 172.^*\); I.A. Batalin, G.A. Vilkovisky, Existence theorem for gauge algebra, J. Math. Phys. \(26 (1985) 172.^*\) |
| [34] | Batalin, I. A.; Lavrov, P. M.; Tyutin, I. V., Remarks on the Sp(2) covariant lagrangian quantization of gauge theories, J. Math. Phys., 32, 2513 (1991) · Zbl 0825.58063 |
| [35] | I.A. Batalin, K. Bering, P.H. Damgaard, Gauge independence of the Lagrangian path integral in a higher-order formalism Phys. Lett. B 389 (1996) 673 (hep-th/9609037).; I.A. Batalin, K. Bering, P.H. Damgaard, Gauge independence of the Lagrangian path integral in a higher-order formalism Phys. Lett. B 389 (1996) 673 (hep-th/9609037). |
| [36] | I. Batalin, R. Marnelius, General quantum antibrackets, hep-th/9905083.; I. Batalin, R. Marnelius, General quantum antibrackets, hep-th/9905083. · Zbl 0970.81081 |
| [37] | I. Batalin, R. Marnelius, Open group transformations within the Sp(2)-formalism, hep-th/9909223.; I. Batalin, R. Marnelius, Open group transformations within the Sp(2)-formalism, hep-th/9909223. · Zbl 0970.81080 |
| [38] | Baulieu, L.; Thierry-Mieg, J., Algebraic structure of quantum gravity and the classification of the gravitational anomalies, Phys. Lett. B, 145, 53 (1984) |
| [39] | L. Baulieu, Algebraic construction of gauge invariant theories, PAR-LPTHE 84/4 Based on lectures given at Cargèse Summer School: Particles and Fields, Cargèse, France, July 6-22, \(1983.^*\); L. Baulieu, Algebraic construction of gauge invariant theories, PAR-LPTHE 84/4 Based on lectures given at Cargèse Summer School: Particles and Fields, Cargèse, France, July 6-22, \(1983.^*\) |
| [40] | Baulieu, L., Anomalies and gauge symmetry, Nucl. Phys. B, 241, 557 (1984) |
| [41] | Baulieu, L., Perturbative gauge theories, Phys. Rep., 129, 1 (1985) |
| [42] | Baulieu, L.; Becchi, C.; Stora, R., On the covariant quantization of the free bosonic string, Phys. Lett. B, 180, 55 (1986) |
| [43] | Baulieu, L.; Bellon, M.; Grimm, R., BRS symmetry of supergravity in superspace and its projection to component formalism, Nucl. Phys. B, 294, 279 (1987) |
| [44] | Baulieu, L.; Bellon, M., Beltrami parametrization and string theory, Phys. Lett. B, 196, 142 (1987) |
| [45] | Becchi, C.; Rouet, A.; Stora, R., The Abelian Higgs-Kibble model, unitarity of the S operator, Phys. Lett. B, 52, 344 (1974) |
| [46] | Becchi, C.; Rouet, A.; Stora, R., Renormalization of the Abelian Higgs-Kibble model, Commun. Math. Phys., 42, 127 (1975) |
| [47] | C. Becchi, A. Rouet, R. Stora, Renormalization of gauge theories, Ann. Phys. 98 (1976) 287.∗∗∗; C. Becchi, A. Rouet, R. Stora, Renormalization of gauge theories, Ann. Phys. 98 (1976) 287.∗∗∗ |
| [48] | C. Becchi, A. Rouet, R. Stora, Renormalizable theories with symmetry breaking, in: E. Tirapegui (Ed.), Field Theory Quantization and Statistical Physics, Reidel, Dordrecht, 1981 (preprint dated 1975).; C. Becchi, A. Rouet, R. Stora, Renormalizable theories with symmetry breaking, in: E. Tirapegui (Ed.), Field Theory Quantization and Statistical Physics, Reidel, Dordrecht, 1981 (preprint dated 1975). |
| [49] | Becchi, C., On the covariant quantization of the free string: the conformal structure, Nucl. Phys. B, 304, 513 (1988) |
| [50] | F.A. Berends, G.J. Burgers, H. van Dam, On the theoretical problems in constructing interactions involving higher spin massless particles, Nucl. Phys. \(B 260 (1985) 295.^*\); F.A. Berends, G.J. Burgers, H. van Dam, On the theoretical problems in constructing interactions involving higher spin massless particles, Nucl. Phys. \(B 260 (1985) 295.^*\) |
| [51] | K. Bering, P.H. Damgaard, J. Alfaro, Algebra of Higher Antibrackets, Nucl. Phys. B 478 (1996) 459 (hep-th/9604027).; K. Bering, P.H. Damgaard, J. Alfaro, Algebra of Higher Antibrackets, Nucl. Phys. B 478 (1996) 459 (hep-th/9604027). · Zbl 0925.81398 |
| [52] | R.A. Bertlmann, Anomalies in quantum field theory, Clarendon Press, Oxford, UK, 1996, 566 p. (International Series of Monographs on Physics, Vol. 91).; R.A. Bertlmann, Anomalies in quantum field theory, Clarendon Press, Oxford, UK, 1996, 566 p. (International Series of Monographs on Physics, Vol. 91). · Zbl 1223.81003 |
| [53] | P.A. Blaga, L. Tǎtaru, I.V. Vancea, BRST cohomology for 2D gravity, Rom. J. Phys. 40 (1995) 773 (hep-th/9504037).; P.A. Blaga, L. Tǎtaru, I.V. Vancea, BRST cohomology for 2D gravity, Rom. J. Phys. 40 (1995) 773 (hep-th/9504037). · Zbl 1273.81211 |
| [54] | Bonneau, G., Some fundamental but elementary facts on renormalization and regularization: a critical review of the eighties, Int. J. Mod. Phys. A, 5, 3831 (1990) |
| [55] | L. Bonora, P. Cotta-Ramusino, Some remarks On BRS transformations, anomalies and the cohomology of the lie algebra of the group of gauge transformations, Commun. Math. Phys. ((87 (1983) 589.^{*∗}\); L. Bonora, P. Cotta-Ramusino, Some remarks On BRS transformations, anomalies and the cohomology of the lie algebra of the group of gauge transformations, Commun. Math. Phys. ((87 (1983) 589.^{*∗}\) · Zbl 0521.53064 |
| [56] | Bonora, L.; Cotta-Ramusino, P.; Reina, C., Conformal anomaly and cohomology, Phys. Lett. B, 126, 305 (1983) |
| [57] | Bonora, L.; Pasti, P.; Tonin, M., The anomaly structure of theories with external gravity, J. Math. Phys., 27, 2259 (1986) · Zbl 0612.53058 |
| [58] | Bonora, L.; Pasti, P.; Bregola, M., Weyl Cocycles, Class. Quant. Grav., 3, 635 (1986) · Zbl 0615.58046 |
| [59] | Bonora, L.; Pasti, P.; Tonin, M., The chiral anomaly in supersymmetric gauge theories coupled to supergravity, Phys. Lett. B, 167, 191 (1986) |
| [60] | Bourbaki, N., Groupes et Algèbres de Lie I (1960), Hermann: Hermann Paris · Zbl 0199.35203 |
| [61] | Brandt, F.; Dragon, N.; Kreuzer, M., All consistent Yang-Mills Anomalies, Phys. Lett. B, 231, 263 (1989) |
| [62] | Brandt, F.; Dragon, N.; Kreuzer, M., Completeness and nontriviality of the solutions of the consistency conditions, Nucl. Phys. B, 332, 224 (1990) |
| [63] | Brandt, F.; Dragon, N.; Kreuzer, M., Lie algebra cohomology, Nucl. Phys. B, 332, 250 (1990) |
| [64] | Brandt, F.; Dragon, N.; Kreuzer, M., The gravitational anomalies, Nucl. Phys. B, 340, 187 (1990) |
| [65] | F. Brandt, Antifield dependence of anomalies Phys. Lett. B 320 (1994) 57 (hep-th/9310080).; F. Brandt, Antifield dependence of anomalies Phys. Lett. B 320 (1994) 57 (hep-th/9310080). |
| [66] | F. Brandt, Anomaly candidates and invariants of \(D=4,\); F. Brandt, Anomaly candidates and invariants of \(D=4,\) |
| [67] | F. Brandt, W. Troost, A. Van Proeyen, The BRST-antibracket cohomology of \(2d\); F. Brandt, W. Troost, A. Van Proeyen, The BRST-antibracket cohomology of \(2d\) · Zbl 1004.81565 |
| [68] | F. Brandt, W. Troost, A. Van Proeyen, Background charges and consistent continuous deformations of \(2d\); F. Brandt, W. Troost, A. Van Proeyen, Background charges and consistent continuous deformations of \(2d\) · Zbl 1004.81565 |
| [69] | F. Brandt, Local BRST cohomology in minimal \(D=4,\); F. Brandt, Local BRST cohomology in minimal \(D=4,\) |
| [70] | F. Brandt, J. Gomis, J. Simón, Cohomological analysis of bosonic D-strings and 2d sigma models coupled to abelian gauge fields, Nucl. Phys. B 523 (1998) 623 (hep-th/9712125).; F. Brandt, J. Gomis, J. Simón, Cohomological analysis of bosonic D-strings and 2d sigma models coupled to abelian gauge fields, Nucl. Phys. B 523 (1998) 623 (hep-th/9712125). · Zbl 1031.81661 |
| [71] | Browning, A. D.; McMullan, D., The Batalin, Fradkin, and Vilkovisky formalism for higher order theories, J. Math. Phys., 28, 438 (1987) · Zbl 0625.58034 |
| [72] | Bryant, R. L.; Griffiths, P. A., Characteristic cohomology of differential systems I: general theory, J. Am. Math. Soc., 8, 507 (1995) · Zbl 0845.58004 |
| [73] | I.L. Buchbinder, B.R. Mistchuk, V.D. Pershin, BRST - BFV analysis of anomalies in bosonic string theory interacting with background gravitational field, Phys. Lett. B 353 (1995) 457 (hep-th/9502087).; I.L. Buchbinder, B.R. Mistchuk, V.D. Pershin, BRST - BFV analysis of anomalies in bosonic string theory interacting with background gravitational field, Phys. Lett. B 353 (1995) 457 (hep-th/9502087). |
| [74] | Capper, D. M.; Duff, M. J., Trace anomalies in dimensional regularization, Nuovo Cim., 23 A, 173 (1974) |
| [75] | M. Carvalho, L.C. Vilar, C.A. Sasaki, S.P. Sorella, BRS cohomology of zero curvature systems I, the complete ladder case, J. Math. Phys. 37 (1996) 5310 (hep-th/9509047).; M. Carvalho, L.C. Vilar, C.A. Sasaki, S.P. Sorella, BRS cohomology of zero curvature systems I, the complete ladder case, J. Math. Phys. 37 (1996) 5310 (hep-th/9509047). · Zbl 0865.53062 |
| [76] | Chevalley, C.; Eilenberg, S., Cohomology theory of Lie groups and Lie algebras, Trans. Amer. Math. Soc., 63, 85 (1948) · Zbl 0031.24803 |
| [77] | J.C. Collins, Renormalization. An Introduction to Renormalization, the Renormalization Group, and the Operator Product Expansion, University Press, Cambridge, UK, 1984, 380 pp. (Chapter 12.6).; J.C. Collins, Renormalization. An Introduction to Renormalization, the Renormalization Group, and the Operator Product Expansion, University Press, Cambridge, UK, 1984, 380 pp. (Chapter 12.6). · Zbl 1094.53505 |
| [78] | J.C. Collins, R.J. Scalise, The renormalization of composite operators in Yang-Mills theories using general covariant gauge, Phys. Rev. D 50 (1994) 4117 (hep-ph/9403231).; J.C. Collins, R.J. Scalise, The renormalization of composite operators in Yang-Mills theories using general covariant gauge, Phys. Rev. D 50 (1994) 4117 (hep-ph/9403231). |
| [79] | Deser, S.; Duff, M. J.; Isham, C. J., Nonlocal conformal anomalies, Nucl. Phys., B 111, 45 (1976) · Zbl 0967.81529 |
| [80] | Deser, S.; Jackiw, R.; Templeton, S., Three-dimensional massive gauge theories, Phys. Rev. Lett., 48, 975 (1982) |
| [81] | S. Deser, A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 (hep-th/9302047).; S. Deser, A. Schwimmer, Geometric classification of conformal anomalies in arbitrary dimensions, Phys. Lett. B 309 (1993) 279 (hep-th/9302047). |
| [82] | De Wilde, M., On the local chevalley cohomology of the dynamical lie algebra of a symplectic manifold, Lett. Math. Phys., 5, 351 (1981) · Zbl 0476.58012 |
| [83] | B. de Wit, J.W. van Holten, Covariant quantization of gauge theories with open gauge algebra, Phys. Lett. \(79 B (1978) 389.^*\); B. de Wit, J.W. van Holten, Covariant quantization of gauge theories with open gauge algebra, Phys. Lett. \(79 B (1978) 389.^*\) |
| [84] | DeWitt, B. S., Quantum theory of gravity II, the manifestly covariant theory, Phys. Rev., 162, 1195 (1967) · Zbl 0161.46501 |
| [85] | Dickey, L. A., On exactness of the variational bicomplex, Contemp. Math., 132, 307 (1992) · Zbl 0771.58043 |
| [86] | Dixon, J. A.; Taylor, J. C., Renormalization of Wilson operators in gauge theories, Nucl. Phys., B 78, 552 (1974) |
| [87] | J.A. Dixon, Field redefinition and renormalization in gauge theories, Nucl. Phys. \(B 99 (1975) 420.^*\); J.A. Dixon, Field redefinition and renormalization in gauge theories, Nucl. Phys. \(B 99 (1975) 420.^*\) |
| [88] | J.A. Dixon, Cohomology and renormalization of gauge theories, 1, unpublished preprint.; J.A. Dixon, Cohomology and renormalization of gauge theories, 1, unpublished preprint. |
| [89] | J.A. Dixon, Cohomology and renormalization of gauge theories, 2, HUTMP 78/B64.; J.A. Dixon, Cohomology and renormalization of gauge theories, 2, HUTMP 78/B64. |
| [90] | Deans, W. S.; Dixon, J. A., Theory of gauge invariant operators: their renormalization and S matrix elements, Phys. Rev., D 18, 1113 (1978) |
| [91] | Dixon, J.; Ramon Medrano, M., Anomalies of higher-dimension composite fields, Phys. Rev., D 22, 429 (1980) |
| [92] | J.A. Dixon, Calculation of BRS cohomology with spectral sequences, Commun. Math. Phys. ((139 (1991) 495.^{*∗}\); J.A. Dixon, Calculation of BRS cohomology with spectral sequences, Commun. Math. Phys. ((139 (1991) 495.^{*∗}\) · Zbl 0744.53040 |
| [93] | Dragon, N., Regular gravitational Lagrangians, Phys. Lett., B 276, 31 (1992) |
| [94] | N. Dragon, BRS symmetry and cohomology, Lectures given at First National Summer School for Graduate Students, Saalburg 1995, hep-th/\(9602163.^*\); N. Dragon, BRS symmetry and cohomology, Lectures given at First National Summer School for Graduate Students, Saalburg 1995, hep-th/\(9602163.^*\) |
| [95] | N. Dragon, T. Hurth, P. van Nieuwenhuizen, Polynomial form of the Stueckelberg model, Nucl. Phys. Proc. Suppl. 56 B (1997) 318 (hep-th/9703017).; N. Dragon, T. Hurth, P. van Nieuwenhuizen, Polynomial form of the Stueckelberg model, Nucl. Phys. Proc. Suppl. 56 B (1997) 318 (hep-th/9703017). · Zbl 0925.81067 |
| [96] | Dubois-Violette, M.; Talon, M.; Viallet, C. M., New results on BRS cohomology in gauge theory, Phys. Lett., 158 B, 231 (1985) · Zbl 0604.58055 |
| [97] | M. Dubois-Violette, M. Talon, C.M. Viallet, BRS algebras: analysis of the consistency equations in gauge theory, Commun. Math. Phys. ((102 (1985) 105.^{*∗}\); M. Dubois-Violette, M. Talon, C.M. Viallet, BRS algebras: analysis of the consistency equations in gauge theory, Commun. Math. Phys. ((102 (1985) 105.^{*∗}\) · Zbl 0604.58055 |
| [98] | Dubois-Violette, M.; Talon, M.; Viallet, C. M., Anomalous terms in gauge theory: relevance of the structure group, Ann. Inst. Henri Poincaré Phys. Theor., 44, 103 (1986) · Zbl 0604.58057 |
| [99] | Dubois-Violette, M., Systèmes dynamiques contraints: l’approche homologique, Ann. Inst. Fourier, 37, 45 (1987) · Zbl 0635.58007 |
| [100] | Dubois-Violette, M.; Henneaux, M.; Talon, M.; Viallet, C., Some results on local cohomologies in field theory, Phys. Lett., B 267, 81 (1991) |
| [101] | M. Dubois-Violette, M. Henneaux, M. Talon, C. Viallet, General solution of the consistency equation, Phys. Lett. B 289 (1992) 361 (hep-th/9206106).; M. Dubois-Violette, M. Henneaux, M. Talon, C. Viallet, General solution of the consistency equation, Phys. Lett. B 289 (1992) 361 (hep-th/9206106). |
| [102] | Faddeev, L. D.; Popov, V. N., Feynman diagrams for the Yang-Mills field, Phys. Lett., B 25, 29 (1967) |
| [103] | R. Ferrari, P.A. Grassi, Constructive algebraic renormalization of the Abelian Higgs-Kibble model, Phys. Rev. D 60 (1999) 065010 (hep-th/9807191).; R. Ferrari, P.A. Grassi, Constructive algebraic renormalization of the Abelian Higgs-Kibble model, Phys. Rev. D 60 (1999) 065010 (hep-th/9807191). |
| [104] | Feynman, R. P., Quantum theory of gravitation, Acta Phys. Polon., 24, 697 (1963) |
| [105] | Fisch, J.; Henneaux, M.; Stasheff, J.; Teitelboim, C., Existence, uniqueness and cohomology of the classical BRST charge with ghosts of ghosts, Commun. Math. Phys., 120, 379 (1989) · Zbl 0685.58054 |
| [106] | Fisch, J. M.L.; Henneaux, M., Homological perturbation theory and the algebraic structure of the antifield – antibracket formalism for gauge theories, Commun. Math. Phys., 128, 627 (1990) · Zbl 0692.58045 |
| [107] | Fradkin, E. S.; Vilkovisky, G. A., Quantization of relativistic systems with constraints, Phys. Lett., B 55, 224 (1975) · Zbl 0967.81532 |
| [108] | Fradkin, E. S.; Vasilev, M. A., Hamiltonian formalism, quantization and S matrix for supergravity, Phys. Lett., B 72, 70 (1977) · Zbl 0967.81505 |
| [109] | E.S. Fradkin, G.A. Vilkovisky, Quantization of relativistic systems with constraints: equivalence of canonical and covariant formalisms in quantum theory of gravitational field, CERN-TH-2332.; E.S. Fradkin, G.A. Vilkovisky, Quantization of relativistic systems with constraints: equivalence of canonical and covariant formalisms in quantum theory of gravitational field, CERN-TH-2332. · Zbl 0967.81532 |
| [110] | Fradkin, E. S.; Fradkina, T. E., Quantization of relativistic systems with boson and fermion first and second class constraints, Phys. Lett., 72 B, 343 (1978) |
| [111] | Freedman, D. Z.; Townsend, P. K., Antisymmetric tensor gauge theories and nonlinear sigma models, Nucl. Phys., B 177, 282 (1981) · Zbl 0983.81513 |
| [112] | T. Fujiwara, H. Suzuki, K. Wu, Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories, hep-lat/9906015.; T. Fujiwara, H. Suzuki, K. Wu, Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories, hep-lat/9906015. · Zbl 0951.81095 |
| [113] | J.A. Garcia, B. Knaepen, Couplings between generalized gauge fields, Phys. Lett. B 441 (1998) 198 (hep-th/9807016).; J.A. Garcia, B. Knaepen, Couplings between generalized gauge fields, Phys. Lett. B 441 (1998) 198 (hep-th/9807016). |
| [114] | Gel’fand, I. M.; Dorfman, I. Ya., Hamiltonian operators and associated algebraic structures, Funct. Anal. Appl., 13, 174 (1979) · Zbl 0428.58009 |
| [115] | Georgi, H., Thoughts on effective field theory, Nucl. Phys. Proc. Suppl., 29 BC, 1 (1992) |
| [116] | J. Gomis, J. Parı́s, S. Samuel, Antibracket, antifields and gauge theory quantization Phys. Rep. 259 (1995) 1 (hep-th/9412228].\(^*\); J. Gomis, J. Parı́s, S. Samuel, Antibracket, antifields and gauge theory quantization Phys. Rep. 259 (1995) 1 (hep-th/9412228].\(^*\) |
| [117] | Gomis, J.; Parı́s, J., Perturbation theory and locality in the field – antifield formalism, J. Math. Phys., 34, 2132 (1993) · Zbl 0823.58037 |
| [118] | J. Gomis, S. Weinberg, Are nonrenormalizable gauge theories renormalizable? Nucl. Phys. B 469 (1996) 473 (hep-th/9510087).\(^{*∗}\); J. Gomis, S. Weinberg, Are nonrenormalizable gauge theories renormalizable? Nucl. Phys. B 469 (1996) 473 (hep-th/9510087).\(^{*∗}\) · Zbl 1003.81569 |
| [119] | P.A. Grassi, T. Hurth, M. Steinhauser, Practical algebraic renormalization, hep-ph/9907426.; P.A. Grassi, T. Hurth, M. Steinhauser, Practical algebraic renormalization, hep-ph/9907426. · Zbl 0981.81057 |
| [120] | Greub, W.; Halperin, S.; Vanstone, R., (Eilenberg, S.; Bass, H., Connections, Curvature and Cohomology, Vol. III: Cohomology of Principal Bundles and Homogeneous Spaces, Pure and Applied Mathematics. Connections, Curvature and Cohomology, Vol. III: Cohomology of Principal Bundles and Homogeneous Spaces, Pure and Applied Mathematics, (A Series of Monographs and Textbooks), Vol. 47 (1976), Academic Press: Academic Press New York) · Zbl 0372.57001 |
| [121] | M.A. Grigorev, P.H. Damgaard, Superfield BRST charge and the master action, hep-th/9911092.; M.A. Grigorev, P.H. Damgaard, Superfield BRST charge and the master action, hep-th/9911092. |
| [122] | M.A. Grigorev, A.M. Semikhatov, I.Y. Tipunin, BRST formalism and zero locus reduction, hep-th/0001081.; M.A. Grigorev, A.M. Semikhatov, I.Y. Tipunin, BRST formalism and zero locus reduction, hep-th/0001081. |
| [123] | Gugenheim, V. K.A. M.; May, J. P., On the theory and applications of torsion products, Mem. AMS, 142 (1974) · Zbl 0292.55019 |
| [124] | Gugenheim, V. K.A. M., On a perturbation theory for the homology of a loop space, J. Pure Appl. Alg., 25, 197 (1982) · Zbl 0487.55003 |
| [125] | Gugenheim, V. K.A. M.; Stasheff, J. D., On perturbations and \(A_∞\)-structures, Bull. Soc. Math. Belgique, 38, 237 (1986) · Zbl 0639.55008 |
| [126] | Gugenheim, V. K.A. M.; Lambe, L., Applications of perturbation theory to differential homological algebra, Ill. J. Math., 33, 556 (1989) · Zbl 0661.55018 |
| [127] | Gugenheim, V. K.A. M.; Lambe, L.; Stasheff, J. D., Applications of perturbation theory to differential homological algebra II, Ill. J. Math., 34, 485 (1990) · Zbl 0684.55006 |
| [128] | B.W. Harris, J. Smith, Anomalous dimension of the gluon operator in pure Yang-Mills theory, Phys. Rev. D 51 (1995) 4550 (hep-ph/9409405).; B.W. Harris, J. Smith, Anomalous dimension of the gluon operator in pure Yang-Mills theory, Phys. Rev. D 51 (1995) 4550 (hep-ph/9409405). |
| [129] | Henneaux, M., Hamiltonian form of the path integral for theories with a gauge freedom, Phys. Rep., 126, 1 (1985) |
| [130] | Henneaux, M.; Teitelboim, C., BRST cohomology in classical mechanics, Commun. Math. Phys., 115, 213 (1988) · Zbl 0649.58050 |
| [131] | Henneaux, M., Lectures on the antifield - BRST formalism for gauge theories, Lectures given at 20th GIFT Int. Seminar on Theoretical Physics, Jaca, Spain, Jun 5-9, 1989, and at CECS, Santiago, Chile, June/July 1989, Nucl. Phys. B (Proc. Suppl.), A 18, 47 (1990) |
| [132] | Henneaux, M., Space-time locality of the BRST formalism, Commun. Math. Phys., 140, 1 (1991) · Zbl 0734.53067 |
| [133] | M. Henneaux, C. Teitelboim, Quantization of Gauge Systems, University Press, Princeton, USA, 1992, 520 pp.; M. Henneaux, C. Teitelboim, Quantization of Gauge Systems, University Press, Princeton, USA, 1992, 520 pp. · Zbl 0838.53053 |
| [134] | M. Henneaux, Remarks on the renormalization of gauge invariant operators in Yang-Mills theory, Phys. Lett. B 313 (1993) 35 (hep-th/9306101).; M. Henneaux, Remarks on the renormalization of gauge invariant operators in Yang-Mills theory, Phys. Lett. B 313 (1993) 35 (hep-th/9306101). |
| [135] | M. Henneaux, On the gauge-fixed BRST cohomology, Phys. Lett. B 367 (1996) 163 (hep-th/9510116).; M. Henneaux, On the gauge-fixed BRST cohomology, Phys. Lett. B 367 (1996) 163 (hep-th/9510116). |
| [136] | M. Henneaux, Consistent interactions between gauge fields: the cohomological approach, Proceedings of a Conference on Secondary Calculus and Cohomological Physics, August 24-31, 1997, Moscow, Russia, Contemp. Math. 219 (1998) 93 (hep-th/9712226).; M. Henneaux, Consistent interactions between gauge fields: the cohomological approach, Proceedings of a Conference on Secondary Calculus and Cohomological Physics, August 24-31, 1997, Moscow, Russia, Contemp. Math. 219 (1998) 93 (hep-th/9712226). · Zbl 0921.53044 |
| [137] | M. Henneaux, B. Knaepen, C. Schomblond, Characteristic cohomology of p-form gauge theories, Commun. Math. Phys. 186 (1997) 137 (hep-th/9606181).; M. Henneaux, B. Knaepen, C. Schomblond, Characteristic cohomology of p-form gauge theories, Commun. Math. Phys. 186 (1997) 137 (hep-th/9606181). · Zbl 0883.58001 |
| [138] | M. Henneaux, B. Knaepen, C. Schomblond, BRST cohomology of the Chapline-Manton model, Lett. Math. Phys. 42 (1997) 337 (hep-th/9702042).; M. Henneaux, B. Knaepen, C. Schomblond, BRST cohomology of the Chapline-Manton model, Lett. Math. Phys. 42 (1997) 337 (hep-th/9702042). · Zbl 0888.58081 |
| [139] | M. Henneaux, B. Knaepen, All consistent interactions for exterior form gauge fields, Phys. Rev. D 56 (1997) 6076 (hep-th/9706119).; M. Henneaux, B. Knaepen, All consistent interactions for exterior form gauge fields, Phys. Rev. D 56 (1997) 6076 (hep-th/9706119). |
| [140] | M. Henneaux, A. Wilch, Local BRST cohomology of the gauged principal non-linear sigma model, Phys. Rev. D 58 (1998) 025017 (hep-th/9802118).; M. Henneaux, A. Wilch, Local BRST cohomology of the gauged principal non-linear sigma model, Phys. Rev. D 58 (1998) 025017 (hep-th/9802118). |
| [141] | M. Henneaux, B. Knaepen, The Wess-Zumino consistency condition for p-form gauge theories, Nucl. Phys. B 548 (1999) 491 (hep-th/9812140).; M. Henneaux, B. Knaepen, The Wess-Zumino consistency condition for p-form gauge theories, Nucl. Phys. B 548 (1999) 491 (hep-th/9812140). · Zbl 0943.81024 |
| [142] | M. Henneaux, A. Wilch, Semi-invariant terms for gauged non-linear sigma-models, Phys. Lett. B 471 (2000) 373 (hep-th/9906121).; M. Henneaux, A. Wilch, Semi-invariant terms for gauged non-linear sigma-models, Phys. Lett. B 471 (2000) 373 (hep-th/9906121). · Zbl 0959.81009 |
| [143] | Hirsch, G., Sur les groups d’homologie des espaces fibrés, Bull. Soc. Math. Belgique, 6, 79 (1953) · Zbl 0058.38903 |
| [144] | ’t Hooft, G., Renormalization of massless Yang-Mills fields, Nucl. Phys., B 33, 173 (1971) |
| [145] | ’t Hooft, G., Renormalizable lagrangians for massive Yang-Mills fields, Nucl. Phys., B 35, 167 (1971) |
| [146] | ’t Hooft, G.; Veltman, M., Regularization and renormalization of gauge fields, Nucl. Phys., B 44, 189 (1972) |
| [147] | ’t Hooft, G.; Veltman, M., Combinatorics of gauge fields, Nucl. Phys., B 50, 318 (1972) |
| [148] | P.S. Howe, U. Lindström, P. White, Anomalies and renormalization in the BRST-BV framework, Phys. Lett. \(B 246 (1990) 430.^*\); P.S. Howe, U. Lindström, P. White, Anomalies and renormalization in the BRST-BV framework, Phys. Lett. \(B 246 (1990) 430.^*\) |
| [149] | T. Hurth, K. Skenderis, Quantum Noether method, Nucl. Phys. B 541 (1999) 566, hep-th/9803030.; T. Hurth, K. Skenderis, Quantum Noether method, Nucl. Phys. B 541 (1999) 566, hep-th/9803030. · Zbl 0947.81042 |
| [150] | T. Hurth, K. Skenderis, The quantum Noether condition in terms of interacting fields (hep-th/9811231).; T. Hurth, K. Skenderis, The quantum Noether condition in terms of interacting fields (hep-th/9811231). |
| [151] | S.D. Joglekar, B.W. Lee, General theory of renormalization of gauge invariant operators, Ann. Phys. ((97 (1976) 160.^{*∗}\); S.D. Joglekar, B.W. Lee, General theory of renormalization of gauge invariant operators, Ann. Phys. ((97 (1976) 160.^{*∗}\) |
| [152] | R.E. Kallosh, Gauge invariance in supergravitation, Pisma Zh. Eksp. Teor. Fiz. 26 (1977) 575 (in Russian).; R.E. Kallosh, Gauge invariance in supergravitation, Pisma Zh. Eksp. Teor. Fiz. 26 (1977) 575 (in Russian). |
| [153] | Kallosh, R. E., Modified Feynman rules in supergravity, Nucl. Phys., B 141, 141 (1978) |
| [154] | D.B. Kaplan, Effective field theories, Lectures at the Seventh Summer School in Nuclear Physics: Symmetries, Seattle, 1995, nucl-th/9506035.; D.B. Kaplan, Effective field theories, Lectures at the Seventh Summer School in Nuclear Physics: Symmetries, Seattle, 1995, nucl-th/9506035. |
| [155] | Kluberg-Stern, H.; Zuber, J. B., Ward identities and some clues to the renormalization of gauge invariant operators, Phys. Rev., D 12, 467 (1975) |
| [156] | Kluberg-Stern, H.; Zuber, J. B., Renormalization of Nonabelian gauge theories in a background field gauge, 1, green functions, Phys. Rev., D 12, 482 (1975) |
| [157] | H. Kluberg-Stern, J.B. Zuber, Renormalization of Nonabelian gauge theories in a background field gauge, 2, gauge invariant operators, Phys. Rev. D ((12 (1975) 3159.^{*∗}\); H. Kluberg-Stern, J.B. Zuber, Renormalization of Nonabelian gauge theories in a background field gauge, 2, gauge invariant operators, Phys. Rev. D ((12 (1975) 3159.^{*∗}\) |
| [158] | O.M. Khudaverdian, A.P. Nersessian, On the geometry of the Batalin-Vilkovsky formalism, Mod. Phys. Lett. A 8 (1993) 2377 (hep-th/9303136).; O.M. Khudaverdian, A.P. Nersessian, On the geometry of the Batalin-Vilkovsky formalism, Mod. Phys. Lett. A 8 (1993) 2377 (hep-th/9303136). · Zbl 1021.81948 |
| [159] | B. Knaepen, Local BRST cohomology for p-form gauge theories, hep-th/9912021.; B. Knaepen, Local BRST cohomology for p-form gauge theories, hep-th/9912021. |
| [160] | S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Vol. II, section 12, Wiley, New York, 1996.; S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Vol. II, section 12, Wiley, New York, 1996. · Zbl 0119.37502 |
| [161] | Koszul, J.-L., Homologie et cohomologie des algèbres de Lie, Bull. Soc. Math. France, 78, 65-127 (1950) · Zbl 0039.02901 |
| [162] | Lam, Y. P., Perturbation Lagrangian theory for scalar fields: Ward-Takahasi identity and current algebra, Phys. Rev., D 6, 2145 (1972) |
| [163] | Lam, Y. P., Equivalence theorem on Bogoliubov-Parasiuk-Hepp-Zimmermann renormalized lagrangian field theories, Phys. Rev., D 7, 2943 (1973) |
| [164] | Lambe, L.; Stasheff, J. D., Applications of perturbation theory to iterated fibrations, Manus. Math., 58, 363 (1987) · Zbl 0632.55011 |
| [165] | Langouche, F.; Schücker, T.; Stora, R., Gravitational anomalies of the Adler-Bardeen type, Phys. Lett., B 145, 342 (1984) |
| [166] | Lavrov, P. M.; Tyutin, I. V., Effective action in general gauge theories, Sov. J. Nucl. Phys., 41, 1049 (1985) |
| [167] | Lee, B. W.; Zinn-Justin, J., Spontaneously broken gauge symmetries. I. Preliminaries, Phys. Rev., D 5, 3121 (1972) |
| [168] | Lee, B. W.; Zinn-Justin, J., Spontaneously broken gauge symmetries. II. Perturbation theory and renormalization, Phys. Rev., D 5, 3137 (1972) |
| [169] | Lee, B. W.; Zinn-Justin, J., Spontaneously broken gauge symmetries. III. Equivalence, Phys. Rev., D 5, 3155 (1972) |
| [170] | Lee, B. W.; Zinn-Justin, J., Spontaneously broken gauge symmetries. IV. General gauge formulation, Phys. Rev., D 7, 1049 (1973) |
| [171] | Lowenstein, J. H., Differential vertex operations in lagrangian field theory, Commun. Math. Phys., 24, 1 (1971) · Zbl 0221.35008 |
| [172] | Lüscher, M., Topology and the axial anomaly in abelian lattice gauge theories, Nucl. Phys., B 538, 515 (1999) · Zbl 0948.81613 |
| [173] | Mañes, J.; Stora, R.; Zumino, B., Algebraic study of chiral anomalies, Commun. Math. Phys., 102, 157 (1985) · Zbl 0573.53054 |
| [174] | A.V. Manohar, Effective field theories, Lectures at the 1996 Schladming Winter School, hep-ph/9606222.; A.V. Manohar, Effective field theories, Lectures at the 1996 Schladming Winter School, hep-ph/9606222. |
| [175] | McMullan, D., Yang-Mills theory and the Batalin-Fradkin-Vilkovisky formalism, J. Math. Phys., 28, 428 (1987) · Zbl 0615.58035 |
| [176] | Misner, C. W.; Wheeler, J. A., Classical physics as geometry: gravitation, electromagnetism, unquantized charge and mass as properties of curved empty space, Ann. Phys. (NY), 2, 525 (1957) · Zbl 0078.19106 |
| [177] | Olver, P. J., Applications of Lie Groups to Differential Equations (1986), Springer: Springer New York · Zbl 0656.58039 |
| [178] | Zumino, B., Chiral anomalies and differential geometry, (DeWitt, B. S.; Stora, R., Lectures given at Les Houches Summer School on Theoretical Physics, Les Houches, France, August 8-September 2, 1983, published in Relativity, Groups and Topology II (1984), North-Holland: North-Holland Amsterdam) · Zbl 0595.53069 |
| [179] | A. Pich, Effective field theory: course, in: Talk given at Les Houches Summer School in Theoretical Physics, Session 68: Probing the Standard Model of Particle Interactions, Les Houches, France, 28 July-5 September 1997, hep-ph/9806303.; A. Pich, Effective field theory: course, in: Talk given at Les Houches Summer School in Theoretical Physics, Session 68: Probing the Standard Model of Particle Interactions, Les Houches, France, 28 July-5 September 1997, hep-ph/9806303. |
| [180] | Piguet, O.; Rouet, A., Symmetries in perturbative quantum field theory, Phys. Rep., 76, 1 (1981) |
| [181] | O. Piguet, S.P. Sorella, Algebraic renormalization: perturbative renormalization, symmetries and anomalies, Lecture Notes in Physics: m28, Springer, Berlin, Germany, 1995, 134 pp.\(^*\); O. Piguet, S.P. Sorella, Algebraic renormalization: perturbative renormalization, symmetries and anomalies, Lecture Notes in Physics: m28, Springer, Berlin, Germany, 1995, 134 pp.\(^*\) · Zbl 0845.58069 |
| [182] | O. Piguet, S. Wolf, The supercurrent trace identities of the \(N D\); O. Piguet, S. Wolf, The supercurrent trace identities of the \(N D\) · Zbl 0958.81170 |
| [183] | J. Polchinski, Effective field theory and the Fermi surface, Lectures presented at TASI 92, Boulder, CO, June 3-28, 1992, Published in Boulder TASI 92:0235-276 (hep-th/9210046).; J. Polchinski, Effective field theory and the Fermi surface, Lectures presented at TASI 92, Boulder, CO, June 3-28, 1992, Published in Boulder TASI 92:0235-276 (hep-th/9210046). |
| [184] | B. Zumino, Y. Wu, A. Zee, Chiral anomalies, higher dimensions, and differential geometry, Nucl. Phys. \(B 239 (1984) 477.^{*∗}\); B. Zumino, Y. Wu, A. Zee, Chiral anomalies, higher dimensions, and differential geometry, Nucl. Phys. \(B 239 (1984) 477.^{*∗}\) |
| [185] | Saunders, D. J., The Geometry of Jet Bundles (1989), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0665.58002 |
| [186] | Schücker, T., The cohomological proof of Stora’s solutions, Commun. Math. Phys., 109, 167 (1987) · Zbl 0644.58035 |
| [187] | A.A. Slavnov, Ward identities in gauge theories, Theor. Math. Phys. ((10 (1972) 99.^{*∗∗}\); A.A. Slavnov, Ward identities in gauge theories, Theor. Math. Phys. ((10 (1972) 99.^{*∗∗}\) |
| [188] | J. Stasheff, Homological (ghost) approach to constrained Hamiltonian systems, hep-th/9112002.; J. Stasheff, Homological (ghost) approach to constrained Hamiltonian systems, hep-th/9112002. · Zbl 0898.58022 |
| [189] | J. Stasheff, Deformation theory and the Batalin-Vilkovisky master equation, q-alg/9702012.; J. Stasheff, Deformation theory and the Batalin-Vilkovisky master equation, q-alg/9702012. |
| [190] | Sterman, G.; Townsend, P. K.; van Nieuwenhuizen, P., Unitarity, ward identities, and new quantization rules of supergravity, Phys. Rev., D 17, 1501 (1978) |
| [191] | R. Stora, Continuum gauge theories, in: M. Levy, P. Mitter (Eds.), Lectures given at Summer Institute for Theoretical Physics, Cargése, France, July 12-31, 1976, published in New Developments in Quantum Field Theory and statistical Physics, NATO ASI Series B 26, Plenum Press, New York, ((1977.^{*∗}\); R. Stora, Continuum gauge theories, in: M. Levy, P. Mitter (Eds.), Lectures given at Summer Institute for Theoretical Physics, Cargése, France, July 12-31, 1976, published in New Developments in Quantum Field Theory and statistical Physics, NATO ASI Series B 26, Plenum Press, New York, ((1977.^{*∗}\) |
| [192] | R. Stora, Algebraic structure and topological origin of anomalies, in: ’t Hooft et al. (Eds.), Seminar given at Cargèse Summer Institute September 1-15, 1983, published in Progress in Gauge Field Theory, Plenum Press, New York, ((1984.^{*∗}\); R. Stora, Algebraic structure and topological origin of anomalies, in: ’t Hooft et al. (Eds.), Seminar given at Cargèse Summer Institute September 1-15, 1983, published in Progress in Gauge Field Theory, Plenum Press, New York, ((1984.^{*∗}\) |
| [193] | Sullivan, D., Infinitesimal computations in topology, Pub. Math. IHES, 47, 269 (1977) · Zbl 0374.57002 |
| [194] | Takens, F., A global version of the inverse problem to the calculus of variations, J. Differential Geometry, 14, 543 (1979) · Zbl 0463.58015 |
| [195] | H. Suzuki, Anomaly cancellation condition in lattice gauge theory, hep-lat/0002009.; H. Suzuki, Anomaly cancellation condition in lattice gauge theory, hep-lat/0002009. |
| [196] | M. Talon, Algebra of anomalies, PAR-LPTHE-85/37, Presented at Cargèse Summer School, Cargèse, France, July 15-31, 1985.; M. Talon, Algebra of anomalies, PAR-LPTHE-85/37, Presented at Cargèse Summer School, Cargèse, France, July 15-31, 1985. |
| [197] | L. Tǎtaru, I.V. Vancea, BRST cohomology in Beltrami parametrization, Int. J. Mod. Phys. A 11 (1996) 375 (hep-th/9504036).; L. Tǎtaru, I.V. Vancea, BRST cohomology in Beltrami parametrization, Int. J. Mod. Phys. A 11 (1996) 375 (hep-th/9504036). · Zbl 1044.81750 |
| [198] | L. Tǎtaru, R. Tǎtar, Koszul-Tate cohomology for an Sp(2)-covariant quantization of gauge theories with linearly dependent generators, Int. J. Mod. Phys. A 13 (1998) 1981 (hep-th/9708159).; L. Tǎtaru, R. Tǎtar, Koszul-Tate cohomology for an Sp(2)-covariant quantization of gauge theories with linearly dependent generators, Int. J. Mod. Phys. A 13 (1998) 1981 (hep-th/9708159). · Zbl 0925.81081 |
| [199] | J.C. Taylor, Ward identities and charge renormalization of the Yang-Mills field, Nucl. Phys. ((B 33 (1971) 436.^{*∗∗}\); J.C. Taylor, Ward identities and charge renormalization of the Yang-Mills field, Nucl. Phys. ((B 33 (1971) 436.^{*∗∗}\) |
| [200] | Thierry-Mieg, J., Classification of the Yang-Mills anomalies in even and odd dimension, Phys. Lett., B 147, 430 (1984) |
| [201] | Tonin, M., Dimensional regularization and anomalies in chiral gauge theories, Nucl. Phys. Proc. Suppl., 29 BC, 137 (1992) |
| [202] | C.G. Torre, Natural symmetries of the Yang-Mills equations, J. Math. Phys. 36 (1995) 2113 (hep-th/9407129).; C.G. Torre, Natural symmetries of the Yang-Mills equations, J. Math. Phys. 36 (1995) 2113 (hep-th/9407129). · Zbl 0822.53018 |
| [203] | W. Troost, P. van Nieuwenhuizen, A. Van Proeyen, Anomalies and the Batalin-Vilkovisky Lagrangian formalism, Nucl. Phys. \(B 333 (1990) 727.^*\); W. Troost, P. van Nieuwenhuizen, A. Van Proeyen, Anomalies and the Batalin-Vilkovisky Lagrangian formalism, Nucl. Phys. \(B 333 (1990) 727.^*\) |
| [204] | W. Troost, A. Van Proeyen, Regularization, the BV method, and the antibracket cohomology, hep-th/9410162.; W. Troost, A. Van Proeyen, Regularization, the BV method, and the antibracket cohomology, hep-th/9410162. |
| [205] | W. Troost, A. Van Proeyen, Regularization and the BV formalism, hep-th/9307126.; W. Troost, A. Van Proeyen, Regularization and the BV formalism, hep-th/9307126. · Zbl 0844.58090 |
| [206] | Tsujishita, T., On variational bicomplexes associated to differential equations, Osaka J. Math., 19, 311 (1982) · Zbl 0524.58041 |
| [207] | W.M. Tulczyjew, The Euler-Lagrange Resolution, Lecture Notes in Mathematics, Vol. 836, Springer, Berlin, 1980, 22 pp.; W.M. Tulczyjew, The Euler-Lagrange Resolution, Lecture Notes in Mathematics, Vol. 836, Springer, Berlin, 1980, 22 pp. · Zbl 0456.58012 |
| [208] | I.V. Tyutin, Gauge invariance in field theory and statistical physics in operator formalism, LEBEDEV-75-39.; I.V. Tyutin, Gauge invariance in field theory and statistical physics in operator formalism, LEBEDEV-75-39. |
| [209] | I.V. Tyutin, B.L. Voronov, Renormalization of general gauge theories, in: Proceedings, Quantum Gravity∗, Moscow 1981, pp. 481-501.; I.V. Tyutin, B.L. Voronov, Renormalization of general gauge theories, in: Proceedings, Quantum Gravity∗, Moscow 1981, pp. 481-501. |
| [210] | Unruh, W. G., Excluded possibilities of geometrodynamical analog to electric charge, Gen. Relativ. Gravit., 2, 27 (1971) |
| [211] | J.W. van Holten, On the construction of supergravity theories, Ph.D. Thesis, University of Leiden, 1980.; J.W. van Holten, On the construction of supergravity theories, Ph.D. Thesis, University of Leiden, 1980. |
| [212] | A. Verbovetsky, Notes on the horizontal cohomology, in: Proceedings of a Conference on Secondary Calculus and Cohomological Physics, August 24-31, 1997, Moscow, Russia, Contemp. Math. 219 (1998) 211 (math.dg/9803115).; A. Verbovetsky, Notes on the horizontal cohomology, in: Proceedings of a Conference on Secondary Calculus and Cohomological Physics, August 24-31, 1997, Moscow, Russia, Contemp. Math. 219 (1998) 211 (math.dg/9803115). · Zbl 0936.58002 |
| [213] | Vinogradov, A. M., On the algebra-geometric foundations of Lagrangian field theory, Sov. Math. Dokl., 18, 1200 (1977) · Zbl 0403.58005 |
| [214] | Vinogradov, A. M., A spectral sequence associated with a nonlinear differential equation and algebra-geometric foundations of Lagrangian field theory with constraints, Sov. Math. Dokl., 19, 144 (1978) · Zbl 0406.58015 |
| [215] | Vinogradov, A. M., The \(C\)-spectral sequence, Lagrangian formalism, and conservation laws, I, the linear theory. II. The non linear theory, J. Math. Anal. Appl., 100, 1 (1984) · Zbl 0548.58014 |
| [216] | B.L. Voronov, I.V. Tyutin, Formulation of gauge theories of general form, I, Theor. Math. Phys. ((50 (1982) 218.^{*∗}\); B.L. Voronov, I.V. Tyutin, Formulation of gauge theories of general form, I, Theor. Math. Phys. ((50 (1982) 218.^{*∗}\) |
| [217] | B.l. Voronov, I.V. Tyutin, Formulation of gauge theories of general form, II, gauge invariant renormalizability and renormalization structure, Theor. Math. Phys. ((52 (1982) 628.^{*∗}\); B.l. Voronov, I.V. Tyutin, Formulation of gauge theories of general form, II, gauge invariant renormalizability and renormalization structure, Theor. Math. Phys. ((52 (1982) 628.^{*∗}\) |
| [218] | Voronov, B. L.; Lavrov, P. M.; Tyutin, I. V., Canonical transformations and the gauge dependence in general gauge theories, Sov. J. Nucl. Phys., 36, 292 (1982) · Zbl 0588.53079 |
| [219] | Wald, R. M., Spin-two fields and general covariance, Phys. Rev., D 33, 3613 (1986) |
| [220] | Wald, R. M., On identically closed forms locally constructed from a field, J. Math. Phys., 31, 2378 (1990) · Zbl 0728.53064 |
| [221] | Weinberg, S., Phenomenological lagrangians, Physica, 96 A, 327 (1979) |
| [222] | S. Weinberg, The quantum theory of fields. Vol. 1: Foundations, University Press, Cambridge, UK, 1995, 609 pp.; S. Weinberg, The quantum theory of fields. Vol. 1: Foundations, University Press, Cambridge, UK, 1995, 609 pp. · Zbl 0959.81002 |
| [223] | S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, University Press, Cambridge, UK, 1996, 489 pp.; S. Weinberg, The quantum theory of fields. Vol. 2: Modern applications, University Press, Cambridge, UK, 1996, 489 pp. · Zbl 0885.00020 |
| [224] | S. Weinberg, What is quantum field theory, and what did we think it was?, hep-th/9702027.; S. Weinberg, What is quantum field theory, and what did we think it was?, hep-th/9702027. |
| [225] | M. Werneck de Oliveira, M. Schweda, S.P. Sorella, Supersymmetric structure of the bosonic string theory in the Beltrami parametrization, Phys. Lett. B 315 (1993) 93 (hep-th/9305148).; M. Werneck de Oliveira, M. Schweda, S.P. Sorella, Supersymmetric structure of the bosonic string theory in the Beltrami parametrization, Phys. Lett. B 315 (1993) 93 (hep-th/9305148). |
| [226] | J. Wess, B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. ((B 37 (1971) 95.^{*∗∗}\); J. Wess, B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. ((B 37 (1971) 95.^{*∗∗}\) |
| [227] | Witten, E., A note on the antibracket formalism, Mod. Phys. Lett., A 5, 487 (1990) · Zbl 1020.81931 |
| [228] | Yang, C. N.; Mills, R. L., Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev., 96, 191 (1954) · Zbl 1378.81075 |
| [229] | Želobenko, D. P., Compact Lie Groups and their Representations. Compact Lie Groups and their Representations, Translations of Mathematical Monographs, Vol. 40 (1973), American Mathematical Society, Providence: American Mathematical Society, Providence RI · Zbl 0272.22006 |
| [230] | J. Zinn-Justin, Renormalization of gauge theories, in: H. Rollnik, K. Dietz (Eds.), Lectures given at International Summer Institute for Theoretical Physics, July 29-August 9, 1974, Bonn, West Germany, published in Trends in Elementary Particle Physics, Lectures Notes in Physics, Vol. 37, Springer, Berlin, ((1975.^{*∗∗}\); J. Zinn-Justin, Renormalization of gauge theories, in: H. Rollnik, K. Dietz (Eds.), Lectures given at International Summer Institute for Theoretical Physics, July 29-August 9, 1974, Bonn, West Germany, published in Trends in Elementary Particle Physics, Lectures Notes in Physics, Vol. 37, Springer, Berlin, ((1975.^{*∗∗}\) |
| [231] | J. Zinn-Justin, Quantum field theory and critical phenomena, Clarendon press, Oxford, UK, 1989, 914 pp. (International Series of Monographs on Physics, Vol. 77. 3rd Edition 1996 (chapter 21)).; J. Zinn-Justin, Quantum field theory and critical phenomena, Clarendon press, Oxford, UK, 1989, 914 pp. (International Series of Monographs on Physics, Vol. 77. 3rd Edition 1996 (chapter 21)). |
| [232] | J. Zinn-Justin, Renormalization of gauge theories and master equation, Mod. Phys. Lett. A 14 (1999) 1227, hep-th/9906115.; J. Zinn-Justin, Renormalization of gauge theories and master equation, Mod. Phys. Lett. A 14 (1999) 1227, hep-th/9906115. · Zbl 1046.81531 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
