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ON GENERAL LAGRANGIAN FORMULATIONS FOR ARBITRARY MIXED-SYMMETRIC HIGHER-SPIN FERMIONIC FIELDS ON MINKOWSKI BACKGROUNDS // Tomsk State Pedagogical University Bulletin. 2012. Issue 13 (128). P. 139-144

The details of unconstrained Lagrangian formulations (being continuation of earlier developed research for Bose particles in NPB 862 (2012) 270, [arXiv:1110.5044[hep-th]], Phys. of Part. and Nucl. 43 (2012) 689, [arXiv:1202.4710 [hep-th]]) are reviewed for Fermi particles propagated on an arbitrary dimensional Minkowski space-time and described by the unitary irreducible half-integer higher-spin representations of the Poincare group subject to Young tableaux Y (s1; ... ; sk) with k rows. The procedure is based on the construction of the Verma modules and nding auxiliary oscillator realizations for the orthosymplectic osp(kj2k) superalgebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Applying of an universal BRST-BFV approach permit to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive fermionic elds of any spin with appropriate number of gauge and Stukelberg elds. The general construction possesses by the obvious possibility to derive Lagrangians with only holonomic constraints.

Keywords: higher spins, BRST symmetry, Lagrangian formulation, Verma module, gauge invariance

FINITE BRST-ANTIBRST TRANSFORMATIONS FOR THE THEORIES WITH GAUGE GROUP // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 192-197

Following our recent results [P. Yu. Moshin, A. A. Reshetnyak, Nucl. Phys. B 888 (2014) 92], we discuss the notion of finite BRST-antiBRST transformations, with a doublet λa, a = 1, 2, of anticommuting (both global and field-dependent) Grassmann parameters. We find an explicit Jacobian corresponding to this change of variables in the theories with gauge group. Special field-dependent BRST-antiBRST transformations for the Yang-Mills path integral with sa-potential (functionally-dependent) parameters λa = saΛ generated by a finite even-valued functional Λ and the anticommuting generators sa of BRST-antiBRST transformations, amount to a precise change of the gauge-fixing functional. This proves the independence of the vacuum functional under such BRST-antiBRST transformations and leads to presence of modified Ward identities. The form of transformation parameters that induces a change of the gauge in the path integral is found and is exactly evaluated for connecting two arbitrary Rξ-like gauges. The finite field-dependent BRST-antiBRST transformations are used to generalize the Gribov horizon functional h0, in the Landau gauge in BRST-antiBRST setting, in the Gribov– Zwanziger model and to find hξ corresponding to general Rξ-like gauges in the form compatible with gauge-independent S-matrix.

Keywords: gauge theories, BRST-antiBRST Lagrangian quantization, Yang-Mills theory, Gribov–Zwanziger model, field-dependent BRST-antiBRST transformations

BRST-BFV LAGRANGIAN FORMULATIONS FOR HS FIELDS SUBJECT TO TWO-COLUMN YOUNG TABLEAUX // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 213-218

The details of Lagrangian description of irreducible integer higher-spin representations of the Poincare group with an Young tableaux Y [ˆs1, sˆ2] having 2 columns are considered for Bose particles propagated on an arbitrary dimensional Minkowski space-time. The procedure is based, first, on using of an auxiliary Fock space generated by Fermi oscillators (antisymmetric basis), second, on construction of the Verma module and finding auxiliary oscillator realization for sl(2)⊕sl(2) algebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Application of an universal BRST-BFV approach permits to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive mixed-antisymmetric bosonic fields of any spin with appropriate number of gauge and Stukelberg fields. The general prescription possesses by the possibility to derive constrained Lagrangians with only BRST-invariant extended algebraic constraints which describes the Poincare group irreducible representations in terms of mixed-antisymmetric tensor fields with 2 group indices.

Keywords: higher spins, BRST operator, Lagrangian formulation, Verma module, gauge invariance