Derivation of Bessel function closed-form solutions in zero dimensional φ 4 -field theory

The integral is used as an introductory learning tool in the study of Quantum Field Theory and path integrals. Typically, it is analyzed via perturbation theory. Closed-form solutions have been quoted for which I could not find any derivation. Using a simple and elegant transformation, the close for...

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Bibliographic Details
Published in:Heliyon 2023-02, Vol.9 (2), p.e13168
Main Author: Munasinghe, Ranjiva M
Format: Article
Language:English
Online Access:Get full text
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Summary:The integral is used as an introductory learning tool in the study of Quantum Field Theory and path integrals. Typically, it is analyzed via perturbation theory. Closed-form solutions have been quoted for which I could not find any derivation. Using a simple and elegant transformation, the close form solutions for the integral and its even positive integer moments can be obtained in terms of Bessel functions.
ISSN:2405-8440
2405-8440
DOI:10.1016/j.heliyon.2023.e13168