Is the Exponential of the Chern-Simons Action a Normalizable Physical State?

Abstract

We determine the wavefunction that corresponds to the exponential of the Chern-Simons action in a family of gravitational models provided with cosmological constant whose non-perturbative canonical quantization is completely known. We show that this wavefunction does not represent a proper quantum state, because it is not normalizable with respect to the unique inner product of Lorentzian gravity.

13 pages (LATEX), Preprint CGPG-94/2-2

References in corpus (8)

• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Jones Polynomials for Intersecting Knots as Physical States of Quantum Gravity
• Minisuperspaces: Observables and Quantization
• How the Jones Polynomial Gives Rise to Physical States of Quantum General Relativity
• Unique determination of an inner product by adjointness relations in the algebra of quantum observables
• Brst Cohomology and Invariants of 4D Gravity in Ashtekar Variables
• Non-Perturbative Canonical Quantization of Minisuperspace Models: Bianchi Types I and II
• Reality Conditions in Nonperturbative Quantum Cosmology

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• Correlations across horizons in quantum cosmology
• The Chern-Simons state for the non-diagonal Bianchi IX model
• Chern-Simons functional and the no-boundary proposal in Bianchi IX quantum cosmology
• Instanton representation of Plebanski gravity: XIII. Canonical structure of the Petrov classification of nondegenerate spacetimes
• Instanton representation of Plebanski gravity: XVIII. Quantization and proposed resolution of the Kodama state