Practical Introduction to Action-Dependent Field Theories
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915266139521024 |
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| author | de León, Manuel Rifà, Jordi Gaset Muñoz-Lecanda, Miguel C. Rivas, Xavier Román-Roy, Narciso |
| author_facet | de León, Manuel Rifà, Jordi Gaset Muñoz-Lecanda, Miguel C. Rivas, Xavier Román-Roy, Narciso |
| contents | Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a well-defined notion of symmetries and a Noether theorem. This makes them especially suited for open systems. After a conceptual introduction, we make a quick presentation of a new mathematical framework for action-dependent field theory: multicontact geometry. The formalism is illustrated with a variety of action-dependent Lagrangians, some of which are regular and others singular, derived from well-known theories whose Lagrangians have been modified to incorporate action-dependent terms. Detailed computations are provided, including the constraint algorithm for the singular cases, in both the Lagrangian and Hamiltonian formalisms. These are the one-dimensional wave equation, the Klein-Gordon equation and the telegrapher equation, Maxwell's electromagnetism, Metric-affine gravity, the heat equation and Burguers' equation, the Bosonic string theory, and (2+1)-dimensional gravity and Chern-Simons equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Practical Introduction to Action-Dependent Field Theories de León, Manuel Rifà, Jordi Gaset Muñoz-Lecanda, Miguel C. Rivas, Xavier Román-Roy, Narciso High Energy Physics - Theory Mathematical Physics 70S05, 70S10, 53D10, 35R01 Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a well-defined notion of symmetries and a Noether theorem. This makes them especially suited for open systems. After a conceptual introduction, we make a quick presentation of a new mathematical framework for action-dependent field theory: multicontact geometry. The formalism is illustrated with a variety of action-dependent Lagrangians, some of which are regular and others singular, derived from well-known theories whose Lagrangians have been modified to incorporate action-dependent terms. Detailed computations are provided, including the constraint algorithm for the singular cases, in both the Lagrangian and Hamiltonian formalisms. These are the one-dimensional wave equation, the Klein-Gordon equation and the telegrapher equation, Maxwell's electromagnetism, Metric-affine gravity, the heat equation and Burguers' equation, the Bosonic string theory, and (2+1)-dimensional gravity and Chern-Simons equation. |
| title | Practical Introduction to Action-Dependent Field Theories |
| topic | High Energy Physics - Theory Mathematical Physics 70S05, 70S10, 53D10, 35R01 |
| url | https://arxiv.org/abs/2409.08340 |