Quantum Mechanics in Riemannian Space-Times. I. The Canonical Approach

Details Quantum Mechanics in Riemannian Space-Times. I. The Canonical Approach Quantum Mechanics in Riemannian Space-Times. I. The Canonical Approach

1998-12-24

arxiv.org/abs/gr-qc/9812084v2

Grav.Cosmol. 5 (1999) 23-30

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, LaTex 2.09-file, submitted to "Gravitation and Cosmology". Revised in January 06.99 version: addition improving the

Scientific paper

This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the 1+3-formalism is considered, the result of which will be compared in the subsequent paper II with that of the field-theoretical approach, see also gr-qc/9807030. The Schr\"odinger representation of quantum-mechanical kinematics and dynamics is presented in the general-covariant form and a physical interpretation of the state vectors and the position operators is discussed.

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