分次流形上的SUSY规范理论
SUSY gauge theory on graded manifolds
摘要：
利用纤维丛和分次流形，给出了奇偶场的拉格朗日经典场论。特别地，传统的Yang-Mills规范理论是光滑主丛上的联络理论，但它的BRST推广涉及分次流形上的奇鬼场和反场。在这里，我们建立了主分次丛上李超代数的Grassmann分次规范场的Yang-Mills理论。奇规范场的几何定义存在一个问题。我们的目标是分次规范场的杨-米尔斯理论及其BRST推广。
英文摘要：
Lagrangian classical field theory of even and odd fields is adequately formulated in terms of fibre bundles and graded manifolds. In particular, conventional Yang-Mills gauge theory is theory of connections on smooth principal bundles, but its BRST extension involves odd ghost fields an antifields on graded manifolds. Here, we formulate Yang-Mills theory of Grassmann-graded gauge fields associated to Lie superalgebras on principal graded bundles. A problem lies in a geometric definition of odd gauge fields. Our goal is Yang--Mills theory of graded gauge fields and its BRST extension.
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