The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909436774187008 |
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| author | Ciaglia, Florio M. Di Cosmo, Fabio Ibort, Alberto Marmo, Giuseppe Schiavone, Luca Zampini, Alessandro |
| author_facet | Ciaglia, Florio M. Di Cosmo, Fabio Ibort, Alberto Marmo, Giuseppe Schiavone, Luca Zampini, Alessandro |
| contents | We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems (as a (0 + 1)-dimensional field) and more general field theories without gauge symmetries are addressed by showing the existence of a symplectic (and, thus, a Poisson) structure on the space of solutions. Also the easiest case of gauge theory, namely free electrodynamics, is considered: within this problem, a pre-symplectic tensor on the space of solutions is introduced, and a Poisson structure is induced in terms of a flat connection on a suitable bundle associated to the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14136 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics Ciaglia, Florio M. Di Cosmo, Fabio Ibort, Alberto Marmo, Giuseppe Schiavone, Luca Zampini, Alessandro Mathematical Physics Differential Geometry We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems (as a (0 + 1)-dimensional field) and more general field theories without gauge symmetries are addressed by showing the existence of a symplectic (and, thus, a Poisson) structure on the space of solutions. Also the easiest case of gauge theory, namely free electrodynamics, is considered: within this problem, a pre-symplectic tensor on the space of solutions is introduced, and a Poisson structure is induced in terms of a flat connection on a suitable bundle associated to the theory. |
| title | The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics |
| topic | Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2208.14136 |