تقرير
The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics
| العنوان: | The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics |
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| المؤلفون: | Ciaglia, Florio M., Di Cosmo, Fabio, Ibort, Alberto, Marmo, Giuseppe, Schiavone, Luca, Zampini, Alessandro |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics, Mathematics - Differential Geometry |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2208.14136 |
| رقم الأكسشن: | edsarx.2208.14136 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |