First order formalism for quantum gravity
We develop a first order formalism for the quantization of gravity. We take as canonical variables both the induced metric and the extrinsic curvature of the (d - 1) -dimensional hypersurfaces obtained by the foliation of the d - dimensional spacetime. After solving the constraint algebra we use the Dirac formalism to quantize the theory and obtain a new representation for the Wheeler-DeWitt equation, defined in the functional space of the extrinsic curvature. We also show how to obtain several different representations of the Wheeler-DeWitt equation by considering actions differing by a total divergence. In particular, the intrinsic and extrinsic time approaches appear in a natural way, as do equivalent representations obtained by functional Fourier transforms of appropriate variables. We conclude with some remarks about the construction of the Hilbert space within the first order formalism. 10 refs.
- Research Organization:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- DOE Contract Number:
- AC02-76CH03000
- OSTI ID:
- 6507242
- Report Number(s):
- FNAL/Pub-87/73-A; ON: DE87009651
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
GRAVITATIONAL FIELDS
QUANTIZATION
DIRAC COSMOLOGY
DIRAC OPERATORS
FOURIER TRANSFORMATION
HILBERT SPACE
METRICS
SPACE-TIME
BANACH SPACE
COSMOLOGY
INTEGRAL TRANSFORMATIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
QUANTUM OPERATORS
SPACE
TRANSFORMATIONS
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation