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Title: First order formalism for quantum gravity

Abstract

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.

Authors:
; ;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
OSTI Identifier:
6507242
Report Number(s):
FNAL/Pub-87/73-A
ON: DE87009651
DOE Contract Number:  
AC02-76CH03000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, 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

Citation Formats

Gleiser, M, Holman, R, and Neto, N P. First order formalism for quantum gravity. United States: N. p., 1987. Web. doi:10.2172/6507242.
Gleiser, M, Holman, R, & Neto, N P. First order formalism for quantum gravity. United States. https://doi.org/10.2172/6507242
Gleiser, M, Holman, R, and Neto, N P. 1987. "First order formalism for quantum gravity". United States. https://doi.org/10.2172/6507242. https://www.osti.gov/servlets/purl/6507242.
@article{osti_6507242,
title = {First order formalism for quantum gravity},
author = {Gleiser, M and Holman, R and Neto, N P},
abstractNote = {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.},
doi = {10.2172/6507242},
url = {https://www.osti.gov/biblio/6507242}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri May 01 00:00:00 EDT 1987},
month = {Fri May 01 00:00:00 EDT 1987}
}