Relativistic mechanics, cosymplectic manifolds and symmetries

Abstract

We consider the formulation by Jany\vska 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.