Finite energy quantization on a topology changing spacetime

TL;DR

This paper investigates quantum field behavior in the topology-changing trousers spacetime, demonstrating that previous divergences are artifacts of the quantization scheme and can be avoided with an alternative approach.

Contribution

It shows that the divergence found in earlier studies is due to the choice of Fock space, and proposes a different quantization scheme that yields bounded stress-energy tensor components.

Findings

Previous divergences are artifacts of the Fock space choice.

Alternative quantization yields finite stress-energy components.

Supports the idea that topology change may be consistent in quantum gravity.

Abstract

The "trousers" spacetime is a pair of flat 2D cylinders ("legs") merging into into a single one ("trunk"). In spite of its simplicity this spacetime has a few features (including, in particular, a naked singularity in the "crotch") each of which is presumably unphysical, but for none of which a mechanism is known able to prevent its occurrence. Therefore it is interesting and important to study the behavior of the quantum fields in such a space. Anderson and DeWitt were the first to consider the free scalar field in the trousers spacetime. They argued that the crotch singularity produces an infinitely bright flash, which was interpreted as evidence that the topology of space is dynamically preserved. Similar divergencies were later discovered by Manogue, Copeland and Dray who used a more exotic quantization scheme. Later yet the same result obtained within a somewhat different approach led Sorkin to the conclusion that the topological transition in question is suppressed in quantum gravity. In this paper I show that the Anderson--DeWitt divergence is an artifact of their choice of the Fock space. By choosing a different one-particle Hilbert space one gets a quantum state in which the components of the stress-energy tensor (SET) are bounded in the frame of a free-falling observer.