On the characterization of infinitesimal symmetries of the relativistic phase space
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Physics A: Mathematical and Theoretical |
| MU Faculty or unit | |
| Citation | |
| Web | http://iopscience.iop.org/1751-8121/45/48/485205 |
| Doi | http://dx.doi.org/10.1088/1751-8113/45/48/485205 |
| Field | Theoretical physics |
| Keywords | Relativistic mechanics; jets of submanifolds; nonlinear connections; contact forms; cosymplectic forms; infinitesimal symmetries |
| Attached files | |
| Description | The phase space of relativistic particle mechanics is defined as the first jet space of motions regarded as time-like one-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally a generalized contact structure on the odd-dimensional phase space. In the paper, infinitesimal symmetries of the phase structures are characterized. More precisely, it is proved that all phase infinitesimal symmetries are special Hamiltonian lifts of distinguished conserved quantities on the phase space. It is proved that generators of infinitesimal symmetries constitute a Lie algebra with respect to a special bracket. A momentum map for groups of symmetries of the geometric structures is provided. |
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