标题： BV形式主义：理论与矩阵模型的应用 显示英文标题

标题： The BV formalism: theory and application to a matrix model

摘要： 我们回顾在$0$维规范理论背景下的BV形式主义。 对于具有仿射配置空间$X_{0}$的规范理论$(X_{0}, S_{0})$，我们描述了一个构造相应扩展理论$(\tilde{X}, \tilde{S})$的算法，该理论通过引入鬼场和反鬼场得到，其中$\tilde{S}$是$\mathcal{O}_{\tilde{X}}$中的经典主方程的解。 此构造是定义与$(\tilde{X}, \tilde{S})$相关的（规范固定）BRST上同调复形的第一步，它编码了初始规范理论的许多有趣信息$(X_{0}, S_{0})$。本文的第二部分致力于将此方法应用于具有$U(2)$规范对称性的矩阵模型，明确确定相应的$\tilde{X}$以及该模型的经典主方程的一般解$\tilde{S}$。 显示英文摘要

摘要： 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.