A $k$-contact Geometrical Approach to Pseudo-Gauge Transformation
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912704847937536 |
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| author | Hontarenko, Mykhailo de Lucas, Javier Maskalaniec, Adam |
| author_facet | Hontarenko, Mykhailo de Lucas, Javier Maskalaniec, Adam |
| contents | We propose a starting point to the geometric description for the pseudo-gauge ambiguity in relativistic hydrodynamics, showing that it corresponds to the freedom to redefine the thermodynamic equilibrium state of the system. To do this, we develop for the first time a description of a relativistic hydrodynamic-like theory using $k$-contact geometry. In this approach, thermodynamic laws are encoded in a $k$-contact form, thermodynamical states are described via $k$-contact Legendrian submanifolds, and conservation laws emerge as a consequence of Hamilton-de Donder-Weyl (HdDW) equations. The inherent non-uniqueness of these solutions is identified as the source of the pseudo-gauge freedom. We explicitly demonstrate how this redefinition of equilibrium works in a model of a Bjorken-like expansion, where a pseudo-gauge transformation is shown to leave the physical dissipation invariant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $k$-contact Geometrical Approach to Pseudo-Gauge Transformation Hontarenko, Mykhailo de Lucas, Javier Maskalaniec, Adam Mathematical Physics High Energy Physics - Theory Differential Geometry 53D10, 53Z05 (Primary) We propose a starting point to the geometric description for the pseudo-gauge ambiguity in relativistic hydrodynamics, showing that it corresponds to the freedom to redefine the thermodynamic equilibrium state of the system. To do this, we develop for the first time a description of a relativistic hydrodynamic-like theory using $k$-contact geometry. In this approach, thermodynamic laws are encoded in a $k$-contact form, thermodynamical states are described via $k$-contact Legendrian submanifolds, and conservation laws emerge as a consequence of Hamilton-de Donder-Weyl (HdDW) equations. The inherent non-uniqueness of these solutions is identified as the source of the pseudo-gauge freedom. We explicitly demonstrate how this redefinition of equilibrium works in a model of a Bjorken-like expansion, where a pseudo-gauge transformation is shown to leave the physical dissipation invariant. |
| title | A $k$-contact Geometrical Approach to Pseudo-Gauge Transformation |
| topic | Mathematical Physics High Energy Physics - Theory Differential Geometry 53D10, 53Z05 (Primary) |
| url | https://arxiv.org/abs/2511.09375 |