Third quantization and the Wheeler-DeWitt equation
Beginning with a proposal for the normalization of solutions to the Wheeler-DeWitt equation put forth by DeWitt we argue that the Wheeler-DeWitt equation naturally lends itself to a second quantization in analogy to the second quantization of the Klein-Gordon equation. We identify a conserved current, as well as DeWitt's proposal for normalization, as coming from a Lagrangian which is the analog of a second-quantized string theory whose spatial coordinates parametrize the coset manifold SL(3,R)/SO(3). We derive a mode decomposition of the second-quantized Wheeler-DeWitt field in the linearized approximation to quantum gravity, the zero modes of which are given by the total three-volume as well as various anisotropy parameters. We discuss the possibility of adding topological interactions for the linearized theory and find a representation in terms of vertex operators. In a two-dimensional setting we discuss a connection between our formalism and a proposal by Green which may shed light on some of the interpretational problems of string theory.
- Research Organization:
- The Rockefeller University, 1230 York Avenue, New York, New York 10021
- OSTI ID:
- 6694238
- Journal Information:
- Phys. Rev. D; (United States), Vol. 38:10
- Country of Publication:
- United States
- Language:
- English
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GENERAL PHYSICS
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STRING MODELS
QUANTIZATION
COSMOLOGY
DIFFERENTIAL EQUATIONS
FIELD THEORIES
KLEIN-GORDON EQUATION
LAGRANGIAN FUNCTION
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SCALAR FIELDS
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COMPOSITE MODELS
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EXTENDED PARTICLE MODEL
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LIE GROUPS
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PARTIAL DIFFERENTIAL EQUATIONS
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645400* - High Energy Physics- Field Theory
657003 - Theoretical & Mathematical Physics- Relativity & Gravitation