Finite states in four dimensional quantized gravity

Details Finite states in four dimensional quantized gravity Finite states in four dimensional quantized gravity

2007-03-08

arxiv.org/abs/gr-qc/0703052v6

Class.Quant.Grav.25:125001,2008; Class.Quant.Grav.25:125002,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/25/12/125001 1

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.

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