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General Relativity and Quantum Cosmology

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

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.
Comments: 25 pages, no figures, Latex file. Revised version
Journal reference: Gen.Rel.Grav. 33 (2001) 1-28
DOI: 10.1023/A:1002067601136
Cite as: arXiv:gr-qc/0002023
  (or arXiv:gr-qc/0002023v2 for this version)

Submission history

From: Merced Montesinos [view email]
[v1] Fri, 4 Feb 2000 17:13:26 UTC (18 KB)
[v2] Tue, 16 Jan 2001 18:51:52 UTC (18 KB)