The phase space of relativistic particle mechanics is defined as the 1st jet
space of motions regarded as timelike 1-dimensional submanifolds of spacetime.
A Lorentzian metric and an electromagnetic 2-form define naturally on the
odd-dimensional phase space a generalized contact structure. 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.Comment: 38 page
