The BV formalism: theory and application to a matrix model

Abstract

We review the BV formalism in the context of $0$-dimensional gauge theories. For a gauge theory $(X_0,S_0)$ with an affine configuration space $X_0$, we describe an algorithm to construct a corresponding extended theory $(\tilde{X},\tilde{S})$, obtained by introducing ghost and anti-ghost fields, with $\tilde{S}$ a solution of the classical master equation in ${\mathcal{O}}_{\tilde{X}}$. This construction is the first step to define the (gauge-fixed) BRST cohomology complex associated to $(\tilde{X},\tilde{S})$, which encodes many interesting information on the initial gauge theory $(X_0,S_0)$. The second part of this article is devoted to the application of this method to a matrix model endowed with a $U(2)$-gauge symmetry, explicitly determining the corresponding $\tilde{X}$ and the general solution $\tilde{S}$ of the classical master equation for the model.

References in corpus (2)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism
• An introduction to the Batalin-Vilkovisky formalism

Cited by in corpus (5)

• Noncommutative geometry and the BV formalism: application to a matrix model
• One-loop corrections to the spectral action
• Batalin-Vilkovisky quantization of fuzzy field theories
• BV quantization of dynamical fuzzy spectral triples
• The BRST cohomology and a generalized Lie algebra cohomology: analysis of a matrix model