Lagrangian Sp(3) BRST symmetry for irreducible gauge theories. (English) Zbl 1009.81067
The authors show that the methods of homological perturbation theory can be extended in order to cover the construction of the Lagrangian Sp(3) BRST symmetry in the irreducible case. This is done by triplicating each differential appearing in the antibracket-antifield BRST formalism. The correct ghost spectrum is determined by the triplication of the gauge transformations of a given irreducible theory. Then a proper construction of the exterior longitudinal tricomplex is developed to ensure that the cohomologies associated with each of the three exterior longitudinal derivatives are isomorphic to the cohomology of the standard exterior longitudinal derivative along the gauge orbits from the BRST description of the initial irreducible theory. It is shown that the canonical generator of the Sp(3) BRST algebra, which is a solution to the classical master equation of the Sp(3) formalism, exists. Finally a gauge-fixing procedure providing the invariance of the effective action with respect to BRST symmetries is constructed.
Reviewer: Viktor Abramov (Tartu)
MSC:
| 81T70 | Quantization in field theory; cohomological methods |
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
References:
| [1] | DOI: 10.1016/0370-2693(74)90058-6 · doi:10.1016/0370-2693(74)90058-6 |
| [2] | DOI: 10.1016/0370-2693(75)90448-7 · Zbl 0967.81532 · doi:10.1016/0370-2693(75)90448-7 |
| [3] | DOI: 10.1016/0370-2693(77)90553-6 · doi:10.1016/0370-2693(77)90553-6 |
| [4] | DOI: 10.1016/0370-2693(78)90135-1 · doi:10.1016/0370-2693(78)90135-1 |
| [5] | DOI: 10.1016/0370-2693(83)90784-0 · Zbl 0967.81508 · doi:10.1016/0370-2693(83)90784-0 |
| [6] | DOI: 10.1016/0370-1573(85)90103-6 · doi:10.1016/0370-1573(85)90103-6 |
| [7] | DOI: 10.1016/0370-2693(81)90205-7 · doi:10.1016/0370-2693(81)90205-7 |
| [8] | DOI: 10.1016/0370-2693(83)90645-7 · doi:10.1016/0370-2693(83)90645-7 |
| [9] | Batalin I. A., Phys. Rev. 28 pp 2567– (1983) |
| [10] | DOI: 10.1063/1.526780 · doi:10.1063/1.526780 |
| [11] | DOI: 10.1016/0370-1573(94)00112-G · doi:10.1016/0370-1573(94)00112-G |
| [12] | Hirsch G., Bull. Soc. Math. Belg. 6 pp 79– (1953) |
| [13] | Stasheff J. D., Trans. Am. Math. Soc. 108 pp 293– (1963) |
| [14] | DOI: 10.1016/0022-4049(82)90036-6 · Zbl 0487.55003 · doi:10.1016/0022-4049(82)90036-6 |
| [15] | Gugenheim V. K. A. M., Bull. Soc. Math. Belg. 38 pp 237– (1986) |
| [16] | DOI: 10.1007/BF01165893 · Zbl 0632.55011 · doi:10.1007/BF01165893 |
| [17] | DOI: 10.1090/S0273-0979-1988-15645-5 · Zbl 0669.18009 · doi:10.1090/S0273-0979-1988-15645-5 |
| [18] | DOI: 10.1007/BF01225504 · Zbl 0685.58054 · doi:10.1007/BF01225504 |
| [19] | DOI: 10.1063/1.528828 · Zbl 0706.70024 · doi:10.1063/1.528828 |
| [20] | DOI: 10.1063/1.528973 · Zbl 0726.58064 · doi:10.1063/1.528973 |
| [21] | DOI: 10.1016/0370-2693(92)91810-V · doi:10.1016/0370-2693(92)91810-V |
| [22] | DOI: 10.1007/BF02099761 · Zbl 0784.53053 · doi:10.1007/BF02099761 |
| [23] | DOI: 10.1063/1.528742 · Zbl 0716.58035 · doi:10.1063/1.528742 |
| [24] | DOI: 10.1063/1.529517 · Zbl 0825.58063 · doi:10.1063/1.529517 |
| [25] | DOI: 10.1016/0370-2693(92)90654-M · doi:10.1016/0370-2693(92)90654-M |
| [26] | DOI: 10.1088/0305-4470/26/21/045 · Zbl 0817.58015 · doi:10.1088/0305-4470/26/21/045 |
| [27] | DOI: 10.1016/0550-3213(83)90479-0 · doi:10.1016/0550-3213(83)90479-0 |
| [28] | Spiridonov V. P., Nucl. Phys. 308 pp 257– (1988) · doi:10.1016/0550-3213(88)90576-7 |
| [29] | DOI: 10.1016/0550-3213(90)90598-8 · doi:10.1016/0550-3213(90)90598-8 |
| [30] | DOI: 10.1016/0550-3213(90)90583-Y · doi:10.1016/0550-3213(90)90583-Y |
| [31] | DOI: 10.1142/S0217732390002122 · Zbl 1020.81920 · doi:10.1142/S0217732390002122 |
| [32] | DOI: 10.1016/0550-3213(91)90224-L · doi:10.1016/0550-3213(91)90224-L |
| [33] | DOI: 10.1016/0370-2693(94)91316-1 · doi:10.1016/0370-2693(94)91316-1 |
| [34] | DOI: 10.1088/0305-4470/28/14/032 · Zbl 0860.58047 · doi:10.1088/0305-4470/28/14/032 |
| [35] | DOI: 10.1142/S0217751X9800086X · Zbl 0925.81081 · doi:10.1142/S0217751X9800086X |
| [36] | DOI: 10.1063/1.532019 · Zbl 0878.58055 · doi:10.1063/1.532019 |
| [37] | DOI: 10.1016/S0370-2693(97)01356-7 · doi:10.1016/S0370-2693(97)01356-7 |
| [38] | DOI: 10.1142/S0217732300001341 · doi:10.1142/S0217732300001341 |
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.
