The fermionic particle density of flat (1 + 1)- dimensional spacetime seen by an arbitrarily moving observer

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 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’.