Relational evolution of the degrees of freedom of generally covariant quantum theories

Preprint

16 January 2001

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.gr-qc/0002023

Abstract

We study the classical and quantum dynamics of generally covariant theories with vanishing a Hamiltonian and with a finite number of degrees of freedom. In particular, the geometric meaning of the full solution of the relational evolution of the degrees of freedom is displayed, which means the determination of the total number of evolving constants of motion required. Also a method to find evolving constants is proposed. The generalized Heinsenberg picture needs M time variables, as opposed to the Heisenberg picture of standard quantum mechanics where one time variable t is enough. As an application, we study the parameterized harmonic oscillator and the SL(2,R) model with one physical degree of freedom that mimics the constraint structure of general relativity where a Schrodinger equation emerges in its quantum dynamics.

Keywords

All Related Versions

Version 1, 2000-02-04, ArXiv
Version 2, 2001-01-16, ArXiv
Published version: General Relativity and Gravitation, 33 (1), 1.

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