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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.17398 |
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| _version_ | 1866911457175666688 |
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| author | Barci, Daniel G. Cugliandolo, Leticia F. Arenas, Zochil González |
| author_facet | Barci, Daniel G. Cugliandolo, Leticia F. Arenas, Zochil González |
| contents | We revisit the construction of the fermionic path-integral representation of overdamped scalar Langevin processes with multiplicative white noise, focusing on the covariance of the generating functional under non-linear changes of variables. We identify the transformations of the auxiliary (commuting and anticommuting) variables that ensure covariance under such transformations. The subtleties induced by the non-differentiable trajectories of the stochastic dynamics are encoded in the fermionic statistics. Upon integrating out the auxiliary variables, we derive the Onsager-Machlup formulation, which agrees with the one recently obtained using a higher-order discretization scheme. In contrast to the latter, the construction proposed here is formulated directly in continuous time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17398 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A covariant fermionic path integral for scalar Langevin processes with multiplicative white noise Barci, Daniel G. Cugliandolo, Leticia F. Arenas, Zochil González Statistical Mechanics We revisit the construction of the fermionic path-integral representation of overdamped scalar Langevin processes with multiplicative white noise, focusing on the covariance of the generating functional under non-linear changes of variables. We identify the transformations of the auxiliary (commuting and anticommuting) variables that ensure covariance under such transformations. The subtleties induced by the non-differentiable trajectories of the stochastic dynamics are encoded in the fermionic statistics. Upon integrating out the auxiliary variables, we derive the Onsager-Machlup formulation, which agrees with the one recently obtained using a higher-order discretization scheme. In contrast to the latter, the construction proposed here is formulated directly in continuous time. |
| title | A covariant fermionic path integral for scalar Langevin processes with multiplicative white noise |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2602.17398 |