Observables, gauge invariance, and time in (2+1)-dimensional quantum gravity

Journal Article · Mon Oct 15 04:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.2647· OSTI ID:6056572

Carlip, S ^[1]

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1. Institute for Advanced Study, Princeton, New Jersey 08540 (USA)

Two formulations of quantum gravity in 2+1 dimensions have been proposed: one based on Arnowitt-Deser-Misner variables and York's extrinsic time,'' the other on diffeomorphism-invariant ISO(2,1) holonomy variables. In the former approach, the Hamiltonian is nonzero, and states are time dependent; in the latter, the Hamiltonian vanishes, and states are time independent but manifestly gauge invariant. This paper compares the resulting quantum theories in order to explore the role of time in quantum gravity. It is shown that the two theories are exactly equivalent for simple spatial topologies, and that gauge-invariant time''-dependent operators can be constructed for arbitrary topologies.

• DOE Contract Number: FG02-90ER40542
• OSTI ID: 6056572
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:8; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FIELD THEORIES
FOUR-DIMENSIONAL CALCULATIONS
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
HAMILTONIANS
HILBERT SPACE
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM OPERATORS
SPACE
THREE-DIMENSIONAL CALCULATIONS
TIME DEPENDENCE
TOPOLOGY