Finite Field-Dependent BRST-antiBRST Transformations: Jacobians and Application to the Standard Model

Abstract

We continue our research Nucl.Phys B888, 92 (2014); Int. J. Mod. Phys. A29, 1450159 (2014); Phys. Lett. B739, 110 (2014); Int. J. Mod. Phys. A30, 1550021 (2015) and extend the class of finite BRST-antiBRST transformations with odd-valued parameters ${\lambda }_a$, $a=1,2$, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-antiBRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-antiBRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-antiBRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits non-trivial solutions leading to a Jacobian equal to unity. Finite BRST-antiBRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters ${\lambda }_a$ is obtained, providing the equivalence of path integrals in any $3$-parameter $R_{\mathbf{\xi }}$-like gauges. The Gribov--Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in $R_{\mathbf{\xi }}$-like gauges, in a gauge-independent way using field-dependent BRST-antiBRST transformations, and in $R_{\mathbf{\xi }}$-like gauges using transverse-like non-Abelian gauge fields.

64 pages, no figures, notes on functional integral, superdeterminants, Eq.(5.30), Ward identities for SM in GZ form (5.43)-(5.45) added, Discussions extended by Proposition 7 and related formulae, Eq.(5.43)-(5.45) corrected, remarks on gauge-invariant regularization, renormalization added, 14 references added, misprints corrected

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Cited by in corpus (16)

• Renormalizability of the Refined Gribov-Zwanziger action in the linear covariant gauges
• The universal character of Zwanziger's horizon function in Euclidean Yang-Mills theories
• Gribov horizon and non-perturbative BRST symmetry in the maximal Abelian gauge
• A non-perturbative study of matter field propagators in Euclidean Yang-Mills theory in linear covariant, Curci-Ferrari and maximal Abelian gauges
• Aspects of the refined Gribov-Zwanziger action in linear covariant gauges
• Remarks on the effects of the Gribov copies on the infrared behavior of higher dimensional Yang-Mills theory
• BRST Symmetry for Torus Knot
• Exploring new horizons of the Gribov problem in Yang-Mills theories
• Finite BRST Mapping in Higher Derivative Models
• Generalization of Faddeev--Popov Rules in Yang--Mills Theories: N=3,4 BRST Symmetries
• Infrared propagators of Yang-Mills-Chern-Simons theories in linear covariant gauges
• On finite $N=1,2$ BRST transformations: Jacobians and Standard Model with gauge-invariant Gribov horizon
• Quantum gauge symmetry of reducible gauge theory
• Gauge copies and the fate of background independence in Yang-Mills theories: a leading order analysis
• Comparative analysis of finite field-dependent BRST transformations
• Non-Abelian gauge theories with composite fields in the background field method