黎曼流形上质量phi_4^4理论的重整化证明
Renormalization Proof for Massive phi_4^4 Theory on Riemannian Manifolds
摘要：
本文基于Wilson重整化群的Wegner-Wilson流方程，采用微扰理论，给出了黎曼流形上有质量$\vp_4^4$理论的归纳重整化性证明.证明手与边界上的扰动Schwinger函数，这意味着树之间的位置参数衰减。一个基本的先决条件是精确的界限上的短期和长期的行为的热核的歧管。借助于正则性假设（通常被认为是理所当然的），我们还证明，对于适当的重整化条件，裸作用量取最小形式，也就是说，除了与标量曲率成比例的几何发散项外，出现与平坦空间中相同的反项。
英文摘要：
In this paper we present an inductive renormalizability proof for massive $\vp_4^4$ theory on Riemannian manifolds, based on the Wegner-Wilson flow equations of the Wilson renormalization group, adapted to perturbation theory. The proof goes in hand with bounds on the perturbative Schwinger functions which imply tree decay between their position arguments. An essential prerequisite are precise bounds on the short and long distance behaviour of the heat kernel on the manifold. With the aid of a regularity assumption (often taken for granted) we also show, that for suitable renormalization conditions the bare action takes the minimal form, that is to say, there appear the same counter terms as in flat space, apart from a logarithmically divergent one which is proportional to the scalar curvature.
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