Finite states in four dimensional quantized gravity

Abstract

This is the first in a series of papers outlining an algorithm to explicitly construct finite quantum states of the full theory of gravity in Ashtekar variables. The algorithm is based upon extending some properties of a special state, the Kodama state for pure gravity with cosmological term, to matter-coupled models. We then illustrate a presciption for nonperturbatively constructing the generalized Kodama states, in preparation for subsequent works in this series. We also introduce the concept of the semiclassical-quantum correspondence (SQC). We express the quantum constraints of the full theory as a system of equations to be solved for the constituents of the `phase' of the wavefunction. Additionally, we provide a variety of representations of the generalized Kodama states including a generalization of the topological instanton term to include matter fields, for which we present arguments for the field-theoretical analogue of cohomology on infinite dimensional spaces. We demonstrate that the Dirac, reduced phase space and geometric quantization procedures are all equivalent for these generalized Kodama states as a natural consequence of the SQC. We relegate the method of the solution to the constraints and other associated ramifications of the generalized Kodama states to separate works.

42 pages: Accepted for publication by Class. Quantum Grav. journal

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Cited by in corpus (7)

• Deformed General Relativity and Torsion
• In Search of Quantum de Sitter Space: Generalizing the Kodama State
• Finite states in four dimensional quantum gravity. The isotropic minisuperspace Asktekar--Klein--Gordon model
• Instanton representation of Plebanski gravity: XIII. Canonical structure of the Petrov classification of nondegenerate spacetimes
• Canonical quantization of Plebanski gravity in diagonal variables
• Instanton representation of Plebanski gravity: XVIII. Quantization and proposed resolution of the Kodama state
• Generalized Kodama partition functions: A preview into normalizability for the generalized Kodama states