Gaussian reference fluid and interpretation of quantum geometrodynamics

Journal Article · Tue Jan 15 04:00:00 EST 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.419· OSTI ID:5988310

Kuchar, K V ^[1]; Torre, C G ^[2]

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1. Department of Physics, University of Utah, Salt Lake City, Utah 84112 (US)
2. Florida Institute of Technology, Melbourne, Florida 32901 (USA)

The Wheeler-DeWitt equation of vacuum geometrodynamics is turned into a Schroedinger equation by imposing the normal Gaussian coordinate conditions with Lagrange multipliers and then restoring the coordinate invariance of the action by parametrization. This procedure corresponds to coupling the gravitational field to a reference fluid. The source appearing in the Einstein law of gravitation has the structure of a heat-conducting dust. When one imposes only the Gaussian time condition but not the Gaussian frame conditions, the heat flow vanishes and the dust becomes incoherent. The canonical description of the fluid uses the Gaussian coordinates and their conjugate momenta as the fluid variables. The energy density and the momentum density of the fluid turn out to be homogeneous linear functions of such momenta. This feature guarantees that the Dirac constraint quantization of the gravitational field coupled to the Gaussian reference fluid leads to a functional Schroedinger equation in Gaussian time. Such an equation possesses the standard positive-definite conserved norm.

• OSTI ID: 5988310
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 43:2; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COUPLING
DIFFERENTIAL EQUATIONS
EINSTEIN FIELD EQUATIONS
ELECTRODYNAMICS
ENERGY-MOMENTUM TENSOR
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GAUSSIAN PROCESSES
GRAVITATIONAL FIELDS
HAMILTONIANS
HEAT FLOW
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
QUANTIZATION
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM OPERATORS
SCHROEDINGER EQUATION
SPACE
SPACE-TIME
TENSORS
UNIVERSE
WAVE EQUATIONS