Finite particle creation in 1+1 dim. compact in space

TL;DR

This paper calculates finite massive particle creation in a 1+1 dimensional compact spacetime, using Bogolubov transformations, revealing that particle production remains finite due to the finite spatial volume.

Contribution

It provides a detailed calculation of particle creation in a compact 1+1D spacetime, demonstrating the finiteness of particle production with explicit Bogolubov transformations.

Findings

Particle creation is finite in a compact 1+1D spacetime.

Bogolubov transformation relates operators between spacelike surfaces.

Particle creation depends on the observer's motion.

Abstract

In this paper we calculate the massive particle creation as seen by a stationary observer in a $1+1$ dimensional spacetime compact in space. The Bogolubov transformation relating the annihilation and creation operators between two spacelike surfaces is calculated. The particle creation, as observed by a stationary observer who moves from the first spacelike surface to the second is then calculated, and shown to be finite, as is expected for a spacetime with finite spatial volume.