(2+1)-dimensional Chern-Simons gravity as a Dirac square root

Journal Article · Fri May 15 00:00:00 EDT 1992 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.45.3584· OSTI ID:7235574

Carlip, S ^[1]

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1. Department of Physics, University of California, Davis, California 95616 (United States)

For simple enough spatial topologies, at least four approaches to (2+1)-dimensional quantum gravity have been proposed: Wheeler-DeWitt quantization, canonical quantization in Arnowitt-Deser-Misner (ADM) variables on reduced phase space, Chern-Simons quantization, and quantization in terms of Ashtekar-Rovelli-Smolin loop variables. An important problem is to understand the relationships among these approaches. By explicitly constructing the transformation between the Chern-Simons and ADM Hilbert spaces, we show here that Chern-Simons quantization naturally gives rise to spinorial wave functions on superspace, whose time evolution is governed by a Dirac equation. Chern-Simons quantum gravity can therefore be interpreted as the Dirac square root of the Wheeler-DeWitt equation.

• OSTI ID: 7235574
• Journal Information: Physical Review, D (Particles Fields); (United States), Vol. 45:10; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
QUANTUM GRAVITY
QUANTIZATION
DIRAC EQUATION
HAMILTONIANS
HILBERT SPACE
KLEIN-GORDON EQUATION
METRICS
PHASE SPACE
SPACE-TIME
SPINORS
THREE-DIMENSIONAL CALCULATIONS
WAVE FUNCTIONS
BANACH SPACE
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SPACE
WAVE EQUATIONS
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)
661100 - Classical & Quantum Mechanics- (1992-)