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Hadamard parametrix of the Feynman Green’s function of a five-dimensional charged scalar field
International Journal of Modern Physics D ( IF 2.2 ) Pub Date : 2020-07-13 , DOI: 10.1142/s0218271820410023
Visakan Balakumar 1 , Elizabeth Winstanley 1
Affiliation  

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 spacetime 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 spacetime dimensions. Even in Minkowski spacetime, 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 spacetime 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 spacetime only.

中文翻译:

五维带电标量场的费曼格林函数的 Hadamard 参数

Hadamard 参数表示弯曲时空背景上量子场的费曼格林函数的短距离奇点结构。减去这些不同的项使费曼格林函数正则化,并能够计算可观察量的重整化期望值。我们研究了五个时空维度中带电、大质量、复杂标量场的 Hadamard 参数。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完全写成封闭形式。因此,我们提出了在 Hadamard 参数矩阵中出现的双标量的协变泰勒级数展开。在一般时空背景下,我们明确说明了计算重整化标量场电流所需的膨胀系数。
更新日期:2020-07-13
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