Derivation of Bessel function closed-form solutions in zero dimensional φ4-field theory
The integral ∫−∞∞e−x2−gx4dx 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...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-02-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844023003754 |
| Summary: | The integral ∫−∞∞e−x2−gx4dx 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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| ISSN: | 2405-8440 |