论文标题
共同学领域理论的数学结构
Mathematical structures of cohomological field theories
论文作者
论文摘要
共同学领域理论的数学框架（cohfts）是用大歧管的语言提出的。研究了Cohfts操作员的代数特性。讨论了构建有或没有仪表对称性的cohfts的方法。特别是，给出了Mathai-Quillen形式主义的概括。诸如拓扑量子力学，拓扑Sigma模型，拓扑M理论和拓扑Yang-Mills理论之类的例子可以使用这种新的形式主义统一获得。
A mathematical framework of cohomological field theories (CohFTs) is formulated in the language of bigraded manifolds. Algebraic properties of operators in CohFTs are studied. Methods of constructing CohFTs, with or without gauge symmetries, are discussed. In particular, a generalization of the Mathai-Quillen formalism is given. Examples such as topological quantum mechanics, topological sigma model, topological M-theory, and topological Yang-Mills theory can be obtained uniformly using this new formalism.
