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.

中文翻译：

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BV 形式主义：矩阵模型的理论和应用

我们在[公式：见正文]维规范理论的背景下回顾了 BV 形式主义。对于具有仿射配置空间[公式：见文本]的规范理论[公式：见文本]，我们描述了一种算法来构造相应的扩展理论[公式：见文本]，通过引入鬼场和反鬼场获得，具有[公式：见正文] [公式：见正文]中经典主方程的解。这种构造是定义与 [公式：见文本] 相关的（规范固定的）BRST 上同调复合体的第一步，它编码了许多关于初始规范理论 [公式：见文本] 的有趣信息。本文的第二部分致力于将该方法应用于具有[公式：见正文]-规范对称性的矩阵模型，明确确定相应的[公式：