The time traveler's guide to the quantization of zero modes

TL;DR

This paper explores how the presence of a time machine influences the quantization of zero modes in a massless scalar field, revealing a unique state prescription and its relation to regularization techniques.

Contribution

It demonstrates a specific zero mode state prescription induced by a time machine and connects it to regularization methods in quantum field theory on curved spacetime.

Findings

Unique zero mode state prescription from time-machine geometry

Relation between zero mode regularization and warp parameter

Connection between vacuum functions and spacetime topology

Abstract

We study the relationship between the quantization of a massless scalar field on the two-dimensional Einstein cylinder and in a spacetime with a time machine. We find that the latter picks out a unique prescription for the state of the zero mode in the Einstein cylinder. We show how this choice arises from the computation of the vacuum Wightman function and the vacuum renormalized stress-energy tensor in the time-machine geometry. Finally, we relate the previously proposed regularization of the zero mode state as a squeezed state with the time-machine warp parameter, thus demonstrating that the quantization in the latter regularizes the quantization in an Einstein cylinder.