CLASSICAL PARTICLE PHASE SPACE IN GENERAL RELATIVITY

Josef Jany\v{s}ka and Marco Modugno

Key words: General relativity, analytical mechanics, jets,
        jet--contact structure, non-linear connections,
        contact structure, co--symplectic forms, quantisation.
1991 Math. Subject Classification: 53C05, 53C15, 58A20, 70H40,
        81S10, 83C10.

Abstract:
The geometric structure of phase space in the Einstein general relativistic
framework is studied. Namely, the jet space of time-like submanifolds of
space-time is introduced and the associated connections, jet--contact and
contact structure are analysed. Moreover, the electromagnetic field is
incorporated in the gravitational structures. A rigorous mathematical
treatment of units of measurement is included as well.

The above setting is regarded as a framework aimed at extending to the
Einstein case a recent quantisation procedure in the Galilei case, based on
jets, connections and co--symplectic forms. According to this purpose, a
structural comparison between Einstein's and Galilei's frameworks is
performed.