scholarly journals LAGRANGIAN Sp(3) BRST SYMMETRY FOR IRREDUCIBLE GAUGE THEORIES

2001 ◽  
Vol 16 (17) ◽  
pp. 2975-3009 ◽  
Author(s):  
C. BIZDADEA ◽  
S. O. SALIU
Keyword(s):  
Perturbation Theory ◽  
Effective Action ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Gauge Fixing ◽  
Homological Perturbation Theory ◽  
Canonical Generator ◽  
Homological Perturbation

The Lagrangian Sp(3) BRST symmetry for irreducible gauge theories is constructed in the framework of homological perturbation theory. The canonical generator of this extended symmetry is shown to exist. A gauge-fixing procedure specific to the standard antibracket–antifield formalism, that leads to an effective action, which is invariant under all the three differentials of the Sp(3) algebra, is given.

scholarly journals On gauge independence for gauge models with soft breaking of BRST symmetry

2014 ◽  
Vol 29 (30) ◽  
pp. 1450184 ◽  
Author(s):  
Alexander Reshetnyak
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Landau Gauge ◽  
Functional Integral ◽  
Yang Mills ◽  
Gauge Models ◽  
S Matrix ◽  
Gauge Fixing ◽  
Dependent Parameter ◽  
Quantum Treatment

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.

From BRST symmetry to the Zinn-Justin equation

2019 ◽  
pp. 237-252
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Gauge Theories ◽  
Brst Symmetry ◽  
Quadratic Equation ◽  
Local Action ◽  
Local Form ◽  
Abelian Gauge ◽  
Brst Cohomology ◽  
Gauge Fixing ◽  
Non Local ◽  
Popov Ghost

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.

Cohomology of Homotopy 2-types

2019 ◽  
pp. 379-422
Author(s):  
Graham Ellis
Keyword(s):  
Perturbation Theory ◽  
Projective Plane ◽  
Integral Homology ◽  
Homotopy Classes ◽  
Cw Complex ◽  
Crossed Modules ◽  
Homological Perturbation Theory ◽  
Homological Perturbation ◽  
Manual Classification

This chapter introduces some of the basic ingredients in the classification of homotopy 2-types and describes datatypes and algorithms for implementing them on a computer. These are illustrated using computer examples involving: the fundamental crossed modules of a CW-complex, cat-1-groups, simplicial groups, Moore complexes, the Dold-Kan correspondence, integral homology of simplicial groups, homological perturbation theory. A manual classification of homotopy classes of maps from a surface to the projective plane is also included.

Cartan's constructions and the twisted Eilenberg–Zilber theorem

2010 ◽  
Vol 17 (1) ◽  
pp. 13-23
Author(s):  
Víctor Álvarez ◽  
José Andrés Armario ◽  
María Dolores Frau ◽  
Pedro Real
Keyword(s):  
Perturbation Theory ◽  
Tensor Product ◽  
Cartesian Product ◽  
Tensor Products ◽  
Standard Product ◽  
Homological Perturbation Theory ◽  
Twisted Tensor Product ◽  
Homological Perturbation ◽  
Twisted Cartesian Product

Abstract Let 𝐺 × τ 𝐺′ be the principal twisted Cartesian product with fibre 𝐺, base 𝐺 and twisting function where 𝐺 and 𝐺′ are simplicial groups as well as 𝐺 × τ 𝐺′; and 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁 (𝐺′) be the twisted tensor product associated to 𝐶𝑁 (𝐺 × τ 𝐺′) by the twisted Eilenberg–Zilber theorem. Here we prove that the pair 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁(𝐺′), μ) is a multiplicative Cartan's construction where μ is the standard product on 𝐶𝑁(𝐺) ⊗ 𝐶𝑁(𝐺′). Furthermore, assuming that a contraction from 𝐶𝑁(𝐺′) to 𝐻𝐺′ exists and using the techniques from homological perturbation theory, we extend the former result to other “twisted” tensor products of the form 𝐶𝑁(𝐺) ⊗ 𝐻𝐺′.

Becchi–Rouet–Stora–Tyutin (BRST) symmetry. Gauge theories: Zinn-Justin equation (ZJ) and renormalization

2021 ◽  
pp. 623-655
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Differential Operator ◽  
Simple Form ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Quantization Method ◽  
Abelian Gauge ◽  
Gauge Action ◽  
Temporal Gauge ◽  
Gauge Fixing ◽  
Popov Ghost

The first part of the chapter describes Faddeev–Popov's quantization method, nd the resulting Slavnov–Taylor (ST) identities, in a simple context. This construction automatically implies, after introduction of Faddeev–Popov ‘ghost’ fermions, a Becchi–Rouet–Stora–Tyutin (BRST) symmetry, whose properties are derived. The differential operator, of fermionic type, representing the BRST symmetry, with a proper choice of variables, has the form of a cohomology operator, and a simple form in terms of Grassmann coordinates. The second part of the chapter is devoted to the quantization and renormalization of non-Abelian gauge theories. Quantization of gauge theories require a gauge-fixing procedure. Starting from the non-covariant temporal gauge, and using a simple identity, one shows the equivalence with a quantization in a general class of gauges, including relativistic covariant gauges. Adapting the formalism developed in the first part, ST identities, and the corresponding BRST symmetry are derived. However, the explicit form of the BRST symmetry is not stable under renormalization. The BRST symmetry implies a more general, quadratic master equation, also called Zinn-Justin (ZJ) equation, satisfied by the quantized action, equation in which gauge and BRST symmetries are no longer explicit. By contrast, in the case of renormalizable gauges, the ZJ equation is stable under renormalization, and its solution yields the general form of the renormalized gauge action.

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