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

TL;DR

This paper investigates whether the exponential of the Chern-Simons action forms a normalizable quantum state in certain gravitational models, concluding it does not due to non-normalizability issues.

Contribution

It provides a non-perturbative analysis of the wavefunction associated with the Chern-Simons action in Lorentzian gravity models with cosmological constant.

Findings

The wavefunction is not normalizable under the Lorentzian inner product.

The exponential of the Chern-Simons action does not constitute a proper quantum state.

Non-normalizability challenges its physical interpretation in these models.

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.