RENORMALIZATION OF GAUGE THEORIES AND MASTER EQUATION

2003 ◽  
Author(s):  
J. ZINN-JUSTIN
Keyword(s):  
Master Equation ◽  
Gauge Theories

scholarly journals THE RELATIONS BETWEEN GENERALIZED FIELDS AND SUPERFIELDS FORMALISMS OF THE BATALIN–VILKOVISKY METHOD OF QUANTIZATION

2004 ◽  
Vol 19 (14) ◽  
pp. 2339-2353 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
General Solution ◽  
Master Equation ◽  
Gauge Theories ◽  
Relativistic Particle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

A general solution of the Batalin–Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin–Vilkovisky master equation is also established. Superfields formalism is usually applied to topological quantum field theories. However, generalized fields method is suitable to find solutions of the Batalin–Vilkovisky master equation either for topological quantum field theories or the usual gauge theories like Yang–Mills theory. We show that by truncating some components of superfields with appropriate actions, generalized fields formalism of the usual gauge theories result. We demonstrate that for some topological quantum field theories and the relativistic particle both of the methods possess the same field contents and yield similar results. Inspired by the observed relations, we give the solution of the BV master equation for on-shell N=1 supersymmetric Yang–Mills theory utilizing superfields.

scholarly journals ON PROBLEMS OF THE LAGRANGIAN QUANTIZATION OF W3-GRAVITY

2003 ◽  
Vol 18 (27) ◽  
pp. 5099-5125
Author(s):  
B. GEYER ◽  
D. M. GITMAN ◽  
P. M. LAVROV ◽  
P. YU. MOSHIN
Keyword(s):  
Master Equation ◽  
Gauge Theories ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Covariant Formalism ◽  
Third Order ◽  
The Third ◽  
Gauge Algebra ◽  
Two Dimensional Model ◽  
General Gauge

We consider the two-dimensional model of W3-gravity within Lagrangian quantization methods for general gauge theories. We use the Batalin–Vilkovisky formalism to study the arbitrariness in the realization of the gauge algebra. We obtain a one-parametric nonanalytic extension of the gauge algebra, and a corresponding solution of the classical master equation, related via an anticanonical transformation to a solution corresponding to an analytic realization. We investigate the possibility of closed solutions of the classical master equation in the Sp (2)-covariant formalism and show that such solutions do not exist in the approximation up to the third order in ghost and auxiliary fields.

scholarly journals CHIRAL BOSONS AS SOLUTIONS OF THE BV MASTER EQUATION FOR 2-D CHIRAL GAUGE THEORIES

1995 ◽  
Vol 10 (19) ◽  
pp. 1365-1374
Author(s):  
N.R.F. BRAGA ◽  
H. MONTANI
Keyword(s):  
Master Equation ◽  
Gauge Group ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Two Dimensional ◽  
Extended Field ◽  
Chiral Bosons

We construct the chiral Wess-Zumino term as a solution for the Batalin-Vilkovisky master equation for anomalous two-dimensional gauge theories, working in an extended field-antifield space, where the gauge group elements are introduced as additional degrees of freedom. We analyze the Abelian and the non-Abelian cases, calculating in both cases the BRST generator in order to show the physical equivalence between this chiral solution for the master equation and the usual (nonchiral) one.

scholarly journals A GENERAL SOLUTION OF THE MASTER EQUATION FOR A CLASS OF FIRST ORDER SYSTEMS

1993 ◽  
Vol 08 (09) ◽  
pp. 811-818 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
Master Equation ◽  
Tensor Field ◽  
Gauge Theories ◽  
Relativistic Particle ◽  
General Procedure ◽  
Kinetic Term ◽  
Yang Mills ◽  
First Order ◽  
Antisymmetric Tensor Field ◽  
Stueckelberg Formalism

Inspired by the formulation of the Batalin-Vilkovisky method of quantization in terms of “odd time,” we show that for a class of gauge theories which are first order in the derivatives, the kinetic term is bilinear in the fields, and the interaction part satisfies some properties, it is possible to give the solution of the master equation in a very simple way. To clarify the general procedure we discuss its application to Yang-Mills theory, massive (Abelian) theory in the Stueckelberg formalism, relativistic particle and to the self-interacting antisymmetric tensor field.

THE WESS–ZUMINO TERM IN THE FIELD–ANTIFIELD FORMALISM

1993 ◽  
Vol 08 (15) ◽  
pp. 2569-2579 ◽  
Author(s):  
N. R. F. BRAGA ◽  
H. MONTANI
Keyword(s):  
Master Equation ◽  
Gauge Theories ◽  
Local Solution ◽  
Generating Functional ◽  
Extended Space ◽  
Brst Charge

We carry out an analysis of the quantization of anomalous gauge theories inside the Batalin–Vilkovisky scheme. Working on the chiral QCD2, we show that by considering the group elements as dynamical variables one is able to construct a local solution, the Wess–Zumino term, for the master equation. Thus the gauge independence of the generating functional is restored. Also, the BRST charge is built up showing that in the extended space this operator recovers the nilpotency.

scholarly journals The BV formalism: Theory and application to a matrix model

2019 ◽  
Vol 31 (10) ◽  
pp. 1950035
Author(s):  
Roberta A. Iseppi
Keyword(s):  
Gauge Theory ◽  
Gauge Symmetry ◽  
General Solution ◽  
Master Equation ◽  
Configuration Space ◽  
Matrix Model ◽  
Gauge Theories ◽  
Brst Cohomology ◽  
Cohomology Complex ◽  
Theory Formula

We review the BV formalism in the context of [Formula: see text]-dimensional gauge theories. For a gauge theory [Formula: see text] with an affine configuration space [Formula: see text], we describe an algorithm to construct a corresponding extended theory [Formula: see text], obtained by introducing ghost and anti-ghost fields, with [Formula: see text] a solution of the classical master equation in [Formula: see text]. This construction is the first step to define the (gauge-fixed) BRST cohomology complex associated to [Formula: see text], which encodes many interesting information on the initial gauge theory [Formula: see text]. The second part of this article is devoted to the application of this method to a matrix model endowed with a [Formula: see text]-gauge symmetry, explicitly determining the corresponding [Formula: see text] and the general solution [Formula: see text] of the classical master equation for the model.

scholarly journals THE BATALIN-VILKOVISKY METHOD OF QUANTIZATION MADE EASY: ODD TIME FORMULATION

1996 ◽  
Vol 11 (01) ◽  
pp. 1-28 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
Master Equation ◽  
Gauge Theories ◽  
Canonical Formalism ◽  
Time Formulation

Odd time was introduced to formulate the Batalin-Vilkovisky method of quantization of gauge theories in a systematic manner. This approach is presented emphasizing the odd time canonical formalism beginning from an odd time Lagrangian. To let beginners have access to the method, essential notions of the gauge theories are briefly discussed, and each step is illustrated with examples. Moreover, the method of solving the master equation in an easy way for a class of gauge theories is reviewed. When this method is applicable some properties of the solutions can easily be extracted, as shown in the related examples.

scholarly journals RENORMALIZATION OF GAUGE THEORIES AND MASTER EQUATION

1999 ◽  
Vol 14 (19) ◽  
pp. 1227-1235 ◽  
Author(s):  
J. ZINN-JUSTIN
Keyword(s):  
Master Equation ◽  
Gauge Theories ◽  
Abelian Gauge ◽  
Evolution Of Ideas ◽  
Brs Symmetry ◽  
Slavnov Taylor Identities

The evolution of ideas which has led from the first proofs of the renormalizability of non-Abelian gauge theories, based on Slavnov–Taylor identities, to the modern proof based on the BRS symmetry and the master equation is recalled. This lecture has been delivered at the Symposium in Honour of Professor C. N. Yang, Stony Brook, May 21, 22, 1999.

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