We consider the formulation by Janyška and Modugno of the phase space of relativistic mechanics in the framework of jets of 1-dimensional time-like submanifolds. Here, the gravitational and electromagnetic structures are encoded in a cosymplectic form. We derive the equation of motion of one relativistic particle in this framework, and prove that the Lagrangian of our model is non-degenerate. This makes the phase space a universal primary constraint. Finally, we show as all symmetries of the equation of motion (including higher or generalized symmetries) can be interpreted as distinguished vector fields on the phase space.
Manno, G., Vitolo, R. (2004). Relativistic mechanics, cosymplectic manifolds and symmetries. NOTE DI MATEMATICA(2), 157-171 [10.1285/i15900932v23n2p157].
Relativistic mechanics, cosymplectic manifolds and symmetries
MANNO, GIOVANNI;
2004
Abstract
We consider the formulation by Janyška and Modugno of the phase space of relativistic mechanics in the framework of jets of 1-dimensional time-like submanifolds. Here, the gravitational and electromagnetic structures are encoded in a cosymplectic form. We derive the equation of motion of one relativistic particle in this framework, and prove that the Lagrangian of our model is non-degenerate. This makes the phase space a universal primary constraint. Finally, we show as all symmetries of the equation of motion (including higher or generalized symmetries) can be interpreted as distinguished vector fields on the phase space.
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