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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | https://arxiv.org/abs/2312.17718 |
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| _version_ | 1866913574704644096 |
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| author | Frasca, Marco Groote, Stefan |
| author_facet | Frasca, Marco Groote, Stefan |
| contents | We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones where the exact solution of the corresponding homogeneous equations can have some known shape. The technique has a formal similarity with the Dyson--Schwinger set of equations to solve quantum field theories. However, there are no physical constraints. Indeed, we show that a complete coincidence with the statistical field model of a quartic scalar theory can be achieved in the Gaussian expansion of the cumulants of the partition function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17718 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some exact Green function solutions for non-linear classical field theories Frasca, Marco Groote, Stefan Mathematical Physics High Energy Physics - Phenomenology High Energy Physics - Theory 81T16, 35A09, 34B27 We consider some non-linear non-homogeneous partial differential equations (PDEs) and derive their exact Green function solution as a functional Taylor expansion in powers of the source. The kind of PDEs we consider are dispersive ones where the exact solution of the corresponding homogeneous equations can have some known shape. The technique has a formal similarity with the Dyson--Schwinger set of equations to solve quantum field theories. However, there are no physical constraints. Indeed, we show that a complete coincidence with the statistical field model of a quartic scalar theory can be achieved in the Gaussian expansion of the cumulants of the partition function. |
| title | Some exact Green function solutions for non-linear classical field theories |
| topic | Mathematical Physics High Energy Physics - Phenomenology High Energy Physics - Theory 81T16, 35A09, 34B27 |
| url | https://arxiv.org/abs/2312.17718 |