The Fermionic Particle Density of Flat 1+1 Dimensional Spacetime seen by an Arbitrarily Moving Observer

TL;DR

This paper develops a coordinate system for arbitrary accelerating observers in 1+1 dimensions to analyze the fermionic particle density of the vacuum, revealing near-thermal spectra under certain conditions.

Contribution

It introduces a general framework for calculating fermionic particle densities for any accelerating observer in 1+1D spacetime, extending previous specific cases.

Findings

Particle density depends on the observer's rapidity function.

Spectrum is nearly thermal for almost uniform acceleration.

Low frequency behavior is influenced by particle horizons.

Abstract

A coordinate system is constructed for a general accelerating observer in 1+1 dimensions, and is used to determine the particle density of the massless Dirac vacuum for that observer. Equations are obtained for the spatial distribution and frequency distribution of massless fermions seen by this observer, in terms of the rapidity function of the observer's worldline. Examples that are considered include the uniformly accelerating observer as a limiting case, but do not always involve particle horizons. Only the low frequency limit depends on the possible presence of particle horizons. The rest of the spectrum is `almost thermal' whenever the observer's acceleration is `almost uniform'.