Generalized Gaussian integrals with application to the Hubbard–Stratonovich transformation

Author:

Byczuk Krzysztof1,Jakubczyk Paweł1

Affiliation:

1. Institute of Theoretical Physics, Faculty of Physics, University of Warsaw , ul. Pasteura 5, PL-02-093 Warszawa, Poland

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.

Publisher

American Association of Physics Teachers (AAPT)

Subject

General Physics and Astronomy

Reference22 articles.

1. Calculation of partition functions;Phys. Rev. Lett.,1959

2. The quantum theory of fields,1995

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