Simplified derivation of the Hawking-Unruh temperature for an accelerated observer in vacuum

Abstract

A detector undergoing uniform acceleration $a$ in a vacuum field responds just as though it were immersed in thermal radiation of temperature $T=\hbar a/2\pi k c$. A simple, intuitive derivation of this result is given for the case of a scalar field in one spatial dimension. The approach is then extended to treat the case where the field seen by the accelerated observer is a spin-1/2 Dirac field.