Wormholes as Basis for the Hilbert Space in Lorentzian Gravity

TL;DR

This paper demonstrates that in Lorentzian gravity, the Hilbert space of quantum states can be spanned by wormhole wave functions, allowing all normalizable states to be interpreted as superpositions of wormholes.

Contribution

It proves that the Hilbert space in Lorentzian gravity admits a basis of wormhole wave functions, establishing a new connection between wormholes and the structure of quantum states.

Findings

Hilbert space admits a basis of wormhole wave functions

Normalizable states can be interpreted as superpositions of wormholes

Constructed a discrete orthonormal basis of wormhole solutions

Abstract

We carry out to completion the quantization of a Friedmann-Robertson-Walker model provided with a conformal scalar field, and of a Kantowski-Sachs spacetime minimally coupled to a massless scalar field. We prove that the Hilbert space determined by the reality conditions that correspond to Lorentzian gravity admits a basis of wormhole wave functions. This result implies that the vector space spanned by the quantum wormholes can be equipped with an unique inner product by demanding an adequate set of Lorentzian reality conditions, and that the Hilbert space of wormholes obtained in this way can be identified with the whole Hilbert space of physical states for Lorentzian gravity. In particular, all the normalizable quantum states can then be interpreted as superpositions of wormholes. For each of the models considered here, we finally show that the physical Hilbert space is separable by constructing a discrete orthonormal basis of wormhole solutions.