Internal Lagrangians and spatial-gauge symmetries
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916489788915712 |
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| author | Druzhkov, Kostya |
| author_facet | Druzhkov, Kostya |
| contents | A direct reformulation of the Hamiltonian formalism in terms of the intrinsic geometry of infinitely prolonged differential equations is obtained. Concepts of spatial equation and spatial-gauge symmetry of a Lagrangian system of equations are introduced. A non-covariant canonical variational principle is proposed and demonstrated using the Maxwell equations as an example. A covariant canonical variational principle is formulated. The results obtained are applicable to any variational equations, including those that do not originate in physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Internal Lagrangians and spatial-gauge symmetries Druzhkov, Kostya Mathematical Physics High Energy Physics - Theory Differential Geometry A direct reformulation of the Hamiltonian formalism in terms of the intrinsic geometry of infinitely prolonged differential equations is obtained. Concepts of spatial equation and spatial-gauge symmetry of a Lagrangian system of equations are introduced. A non-covariant canonical variational principle is proposed and demonstrated using the Maxwell equations as an example. A covariant canonical variational principle is formulated. The results obtained are applicable to any variational equations, including those that do not originate in physics. |
| title | Internal Lagrangians and spatial-gauge symmetries |
| topic | Mathematical Physics High Energy Physics - Theory Differential Geometry |
| url | https://arxiv.org/abs/2404.06606 |