Erratum: Covariant quantization of gauge theories in the framework of extended BRST symmetry [J. Math. Phys. 31, 1487 (1990)]

1991 ◽  
Vol 32 (7) ◽  
pp. 1970-1970
Author(s):  
I. A. Batalin ◽  
P. M. Lavrov ◽  
I. V. Tyutin
1990 ◽  
Vol 31 (6) ◽  
pp. 1487-1493 ◽  
Author(s):  
I. A. Batalin ◽  
P. M. Lavrov ◽  
I. V. Tyutin

Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.


1995 ◽  
Vol 10 (35) ◽  
pp. 2687-2694 ◽  
Author(s):  
P.M. LAVROV ◽  
P.YU. MOSHIN ◽  
A.A. RESHETNYAK

Lagrangian quantization rules for general gauge theories are proposed on a basis of a superfield formulation of the standard BRST symmetry. Independence of the S-matrix on a choice of the gauge is proved. The Ward identities in terms of superfields are derived.


2014 ◽  
Vol 29 (30) ◽  
pp. 1450184 ◽  
Author(s):  
Alexander Reshetnyak

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field–antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional S-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang–Mills and gravity theories. The Gribov–Zwanziger action and the refined Gribov–Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.


1978 ◽  
Vol 79 (4-5) ◽  
pp. 389-393 ◽  
Author(s):  
B. de Wit ◽  
J.W. van Holten

Author(s):  
Jean Zinn-Justin

Chapter 14 contains a general discussion of the quantization and renormalization of non–Abelian gauge theories. The quantization necessitates gauge fixing and introduces the Faddeev–Popov determinant. Slavnov–Taylor identities for vertex (one–particle–irreducible (1PI)) functions, the basis of a first proof of renormalizability, follow. The Faddeev–Popov determinant leads to a non–local action. A local form is generated by introducing Faddeev–Popov ghost fields. The new local action has an important new symmetry, the BRST symmetry. However, the explicit realization of the symmetry is not stable under renormalization. By contrast, a quadratic equation that is satisfied by the action and generating functional of 1PI functions, the Zinn–Justin equation, is stable and at the basis of a general proof of the renormalizability of non–Abelian gauge theories. The proof involves some simple elements of BRST cohomology. The renormalized form of BRST symmetry then makes it possible to prove gauge independence and unitarity.


Author(s):  
Jean Zinn-Justin

Langevin equations for fields have been proposed to describe the dynamics of critical phenomena, or as an alternative method of quantization, which could be useful in cases where ordinary methods lead to difficulties, like in gauge theories. Some of their general properties will be described here. For a number of problems, in particular related to perturbation theory, it is more convenient to work with an action and a field integral than with the equation directly, because standard methods of quantum field theory (QFT) then become available. For this purpose, one can associate a field integral representation, involving a dynamic action to the Langevin equation. The dynamic action can be interpreted as generated by the Langevin equation, considered as a constraint equation. Quite generally, the integral representation of constraint equations, including stochastic equations, leads to an action that has a Slavnov–Taylor (ST) symmetry and, in a different form, has an anticommuting type Becchi–Rouet–Stora–Tyutin (BRST) symmetry, a symmetry that involves anticommuting parameters. This symmetry has no geometric origin, but is merely a consequence of associating a specific form of integral representations to the constraint equations. This symmetry is used in a number of different examples to prove the renormalizability of non-Abelian gauge theories, or to prove the geometric stability of models defined on homogeneous spaces under renormalization. In this chapter, it is used to prove Ward-Takahashi (WT) identities, and to determine how the Langevin equation renormalizes.


1989 ◽  
Vol 196 (1) ◽  
pp. 209-226 ◽  
Author(s):  
Manuel Asorey ◽  
Fernando Falceto

1991 ◽  
Vol 06 (22) ◽  
pp. 2051-2057 ◽  
Author(s):  
P. M. LAVROV

The gauge dependence of the Green's functions generating functionals in the framework of extended Lagrangian BRST quantization is investigated.


1996 ◽  
Vol 11 (17) ◽  
pp. 3097-3125 ◽  
Author(s):  
P.M. LAVROV ◽  
P. YU. MOSHIN ◽  
A.A. RESHETNYAK

Irreducible gauge theories in both the Lagrangian and Hamiltonian versions of the Sp (2)-covariant quantization method are studied. Solutions to generating equations are obtained in the form of expansions in power series of ghost and auxiliary variables up to the third order inclusive.


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