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

The integral [Formula: see text] 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 transform...

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Detalles Bibliográficos
Autor principal: Munasinghe, Ranjiva M.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Elsevier 2023
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9898049/
https://www.ncbi.nlm.nih.gov/pubmed/36747526
http://dx.doi.org/10.1016/j.heliyon.2023.e13168
Descripción
Sumario:The integral [Formula: see text] 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.

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