On the characterization of infinitesimal symmetries of the relativistic phase space

Abstract

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.

38 pages

References in corpus (6)

• On symmetries in Galilei classical mechanics
• Hermitian vector fields and special phase functions
• Killing-Yano tensors and some applications
• Generalized Contact Structures
• Geometric structures of the classical general relativistic phase space
• Geometric aspects of higher order variational principles on submanifolds

Cited by in corpus (1)

• On the geometry of the energy operator in quantum mechanics