×
Barcelos-Neto, J.; De Souza, S. M.

Geometric quantization of topological gauge theories. (English) Zbl 0925.58110

Z. Phys. C 66, No. 1-2, 315-319 (1995).
Summary: We show that Abelian gauge theories in \(2+1\) space-time dimensions with the introduction of a topological Chern-Simons term can be quantized with the use of the symplectic formalism. The consistency of our results are verified by the agreement with the ones from the Dirac case.

Cited in 1 Document

MSC:

58Z05 Applications of global analysis to the sciences
53D50 Geometric quantization
81S10 Geometry and quantization, symplectic methods

Keywords:

geometric quantization; topological gauge theories; Abelian gauge theories; 2+1 spacetime dimensions; topological Chern Simons term; symplectic formalism; pure Chern Simons theory; Maxwell plus Chern Simons theory
Cite Review PDF
Full Text: DOI arXiv

References:

[1] J.F. Schonfeld: Nucl. Phys. B185 (1981) 157; R. Jackiw and S. Templeton, Phys. Rev. D23 (1981) 2291 · doi:10.1016/0550-3213(81)90369-2
[2] S. Deser, R. Jackiw, S. Templeton: Phys. Rev. Lett. 48 (1982) 975 · doi:10.1103/PhysRevLett.48.975
[3] C.R. Hagen: Ann. Phys. 157 (1984) 342. For a general review see R. Mac Kenzie, F. Wilczek: Int. J. Mod. Phys. A3 (1988) 2827 and P. De Sousa Gerbert: Int. J. Mod. Phys. A6 (1991) 173, and references therein · doi:10.1016/0003-4916(84)90064-2
[4] E. Witten: Commun. Math. Phys. 121 (1989) 351 · Zbl 0667.57005 · doi:10.1007/BF01217730
[5] S. Deser, R. Jackiw, S. Templeton: Ann. Phys. 140 (1982) 372 · doi:10.1016/0003-4916(82)90164-6
[6] T. Kimura: Prog. Theor. Phys. 81 (1989) 1109; N. Nakanishi, Int. J. Mod. Phys. A4 (1989) 1055; N. Imai, K. Ishikawa, I. Tanaka: Prog. Theor. Phys. 81 (1989) 758 · doi:10.1143/PTP.81.1109
[7] J.M.F. Labastida, A.V. Ramallo: Phys. Lett. B227 (1989) 92 · doi:10.1016/0370-2693(89)91289-6
[8] P.A.M. Dirac: Can. J. Math. 2 (1950) 129; Lectures on quantum mechanics (Yeshiva University, New York, 1964) · Zbl 0036.14104 · doi:10.4153/CJM-1950-012-1
[9] Q. Lin, G. Ni: Class. Quantum Grav. 7 (1990) 1261 · doi:10.1088/0264-9381/7/7/021
[10] J.M. Martinez-Fern?ndez, C. Wotzasek: Z. Phys. C43 (1989) 305 · doi:10.1007/BF01588219
[11] L.D. Faddeev, R. Jackiw: Phys. Rev. Lett. 60 (1990) 1692 · Zbl 1129.81328 · doi:10.1103/PhysRevLett.60.1692
[12] For a general review on this subject see, for example, N. Woodhouse: Geometric quantization (Clarendon Press, Oxford, 1980)
[13] R. Floreanini, R. Jackiw: Phys. Rev. Lett. 59 (1987) 1873 · doi:10.1103/PhysRevLett.59.1873
[14] J. Govaerts: Int. J. Mod. Phys. A5 (1990) 3625 · Zbl 0709.58018 · doi:10.1142/S0217751X90001574
[15] J. Barcelos-Neto, C. Wotzasek: Mod. Phys. Lett. A7 (1992) 1737; Int. J. Mod. Phys. A7 (1992) 4981; H. Montani: Int. J. Mod. Phys. A8 (1993) 4319 · Zbl 1021.81600 · doi:10.1142/S0217732392001439
[16] Other examples of the symplectic formalism applied in systems with constraints can be found in M.M. Horta-Barreira, C. Wotzasek: Phys. Rev. D45 (1992) 1410; J. Barcelos-Neto, E.S. Cheb-Terrab: Z. Phys. C45 (1992) 133; J. Barcelos-Neto; Phys. Rev. D49 (1994) 1012 · doi:10.1103/PhysRevD.45.1410
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.