五维带电标量场的费曼格林函数的Hadamard参数
Hadamard parametrix of the Feynman Green's function of a five-dimensional charged scalar field
摘要：
阿达玛参数是弯曲时空背景下量子场的费曼格林函数的短距离奇异结构的表示。减去这些发散项使费曼格林函数正规化，并使观测量的重整化期望值的计算成为可能。本文研究了五维时空中带电、大质量、复标量场的Hadamard参量。即使在闵可夫斯基时空中，也不可能将带电标量场的费曼格林函数精确地写成封闭形式。因此，我们提出了协变泰勒级数展开的阿达玛参数中产生的双标量。在一般的时空背景下，我们明确地陈述了重整化标量场电流计算所需的展开系数。这些系数随着展开阶数的增加而变得越来越长，因此我们只给出计算闵可夫斯基时空中重整化应力-能量张量所需的高阶项。
英文摘要：
The Hadamard parametrix is a representation of the short-distance singularity structure of the Feynman Green's function for a quantum field on a curved space-time background. Subtracting these divergent terms regularizes the Feynman Green's function and enables the computation of renormalized expectation values of observables. We study the Hadamard parametrix for a charged, massive, complex scalar field in five space-time dimensions. Even in Minkowski space-time, it is not possible to write the Feynman Green's function for a charged scalar field exactly in closed form. We therefore present covariant Taylor series expansions for the biscalars arising in the Hadamard parametrix. On a general space-time background, we explicitly state the expansion coefficients up to the order required for the computation of the renormalized scalar field current. These coefficients become increasingly lengthy as the order of the expansion increases, so we give the higher-order terms required for the calculation of the renormalized stress-energy tensor in Minkowski space-time only.
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