Third Quantization and the Wheeler-dewitt Equation
Jun, 198871 pages
Published in:
- Phys.Rev.D 38 (1988) 3031-3051
Report number:
- DOE-ER-40325-38
Citations per year
Abstract: (APS)
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.- FIELD EQUATIONS: WHEELER-DEWITT
- Klein-Gordon equation
- QUANTIZATION: 3
- FIELD THEORY: PATH INTEGRAL
- INVARIANCE: REPARAMETRIZATION
- QUANTUM GRAVITY: WAVE FUNCTION
- CHARGE: CONSERVATION LAW
- SPACE-TIME: BOUNDARY CONDITION
- POSTULATED PARTICLE: GRAVITON
- FUNDAMENTAL CONSTANT: LENGTH
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