Renormalised Amperean Area of Brownian Motions and Symanzik Representation of the 2D Abelian Yang--Mills--Higgs Field
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916538351616000 |
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| author | Sauzedde, Isao |
| author_facet | Sauzedde, Isao |
| contents | We construct and study the renormalised Amperean area of a Brownian motion. First studied by W.Werner, the Amperean area is related to Lévy area and stochastic integrals in a way akin to the relation between self-intersection measure and occupation measure. As we explain, it plays a central role in the Symanzik's polymer representation of the continuous Abelian Yang--Mills--Higgs field in 2 dimensions and allows to study this field using classical stochastic calculus and martingale theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16781 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Renormalised Amperean Area of Brownian Motions and Symanzik Representation of the 2D Abelian Yang--Mills--Higgs Field Sauzedde, Isao Probability Mathematical Physics 60J65, 60J55, 81T13, 60H30 We construct and study the renormalised Amperean area of a Brownian motion. First studied by W.Werner, the Amperean area is related to Lévy area and stochastic integrals in a way akin to the relation between self-intersection measure and occupation measure. As we explain, it plays a central role in the Symanzik's polymer representation of the continuous Abelian Yang--Mills--Higgs field in 2 dimensions and allows to study this field using classical stochastic calculus and martingale theory. |
| title | Renormalised Amperean Area of Brownian Motions and Symanzik Representation of the 2D Abelian Yang--Mills--Higgs Field |
| topic | Probability Mathematical Physics 60J65, 60J55, 81T13, 60H30 |
| url | https://arxiv.org/abs/2412.16781 |