Classical particle phase space in general relativity. (English) Zbl 0862.53024

Janyška, Josef; Modugno, Marco

Janyška, Josef (ed.) et al., Differential geometry and applications. Proceedings of the 6th international conference, Brno, Czech Republic, August 28–September 1, 1995. Brno: Masaryk University. 573-602 (1996).

This paper is aimed at transferring to the Einstein spacetime the basic geometrical techniques developed in the Galilei case, in view of a covariant formulation of quantum mechanics in the Einstein framework.
The geometric structure of phase space in this framework is studied; namely, the jet space of timelike submanifolds of spacetime is introduced and the associated connections, jet-contact and contact structures are analysed. Moreover, the electromagnetic field is incorporated in the gravitational structures; a rigorous mathematical treatment of units of measurement is included as well.
For the entire collection see [Zbl 0847.00040].

Reviewer: V.Balan (Bucureşti)

MSC:

53C05	Connections (general theory)
70H40	Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
53C15	General geometric structures on manifolds (almost complex, almost product structures, etc.)
58A20	Jets in global analysis
81S10	Geometry and quantization, symplectic methods
83C10	Equations of motion in general relativity and gravitational theory

Keywords:

general relativity; analytical mechanics; quantisation cosymplectic forms; covariant formulation of quantum mechanics; phase space; jet space; connections; contact structures