Generalized Gaussian integrals with application to the Hubbard–Stratonovich transformation

IF 0.8 4区教育学 Q3 EDUCATION, SCIENTIFIC DISCIPLINES

American Journal of Physics Pub Date : 2023-10-01 DOI:10.1119/5.0141045

Krzysztof Byczuk, Paweł Jakubczyk

引用次数: 0

Abstract

We analyze a variety of Gaussian integrals with the aim of revisiting the derivation of the Hubbard–Stratonovich transformation as given in standard graduate-level textbooks and provide an overview of its applications. We pinpoint problematic steps in the usual discussions and propose careful derivations of the Hubbard–Stratonovich identity pertinent to a variety of situations relevant to statistical physics and quantum field theory. These derivations are based on direct use of either a resolution identity or a series expansion. A few homework problems for students are suggested.

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广义高斯积分及其在Hubbard-Stratonovich变换中的应用

我们分析了各种高斯积分，目的是重新审视Hubbard-Stratonovich变换的推导，在标准的研究生水平的教科书中给出，并提供其应用的概述。我们指出了通常讨论中有问题的步骤，并提出了与统计物理和量子场论相关的各种情况的哈伯德-斯特拉诺维奇恒等式的仔细推导。这些推导是基于直接使用分辨恒等式或级数展开。为学生提出了一些家庭作业问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

American Journal of Physics 物理-物理：综合

CiteScore

1.80

自引率

11.10%

发文量

146

审稿时长

3 months

期刊介绍： The mission of the American Journal of Physics (AJP) is to publish articles on the educational and cultural aspects of physics that are useful, interesting, and accessible to a diverse audience of physics students, educators, and researchers. Our audience generally reads outside their specialties to broaden their understanding of physics and to expand and enhance their pedagogical toolkits at the undergraduate and graduate levels.