Third quantization and the Wheeler-DeWitt equation

Journal Article · Mon Nov 14 23:00:00 EST 1988 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.38.3031· OSTI ID:6694238

McGuigan, M

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), Journal Name: Phys. Rev. D; (United States) Vol. 38:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
657003 -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
COSMOLOGY
DIFFERENTIAL EQUATIONS
EQUATIONS
EXTENDED PARTICLE MODEL
FIELD THEORIES
FUNCTIONS
KLEIN-GORDON EQUATION
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL MODELS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PROBABILITY
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUARK MODEL
SCALAR FIELDS
SCHROEDINGER EQUATION
SO GROUPS
SO-3 GROUPS
STRING MODELS
SYMMETRY GROUPS
U GROUPS
U-1 GROUPS
WAVE EQUATIONS