Radar Time and a State-Space Based Approach To Quantum Field Theory In Gravitational and Electromagnetic Backgrounds

TL;DR

This paper extends a radar time-based formalism for fermionic quantum field theory to include gravitational backgrounds, enabling observer-dependent particle interpretations in dynamic spacetimes without gauge or coordinate ambiguities.

Contribution

It generalizes the radar time approach to non-stationary gravitational backgrounds, providing a consistent, observer-dependent particle interpretation applicable to arbitrary motions and spacetimes.

Findings

Demonstrates consistency with known results in Rindler and de Sitter spaces.

Extends formalism to arbitrary 1+1D spacetimes and 3+1D FRW universes.

Discusses finite volume measurements and particle detection precision.

Abstract

In a recent paper (hep-th/0103228) a new initial value formulation of fermionic QFT was presented that is applicable to an arbitrary observer in any electromagnetic background. This approach suggests a consistent particle interpretation at all times, with the concept of `radar time' used to generalise this interpretation to an arbitrarily moving observer. In the present paper we extend this formalism to allow for gravitational backgrounds. The observer-dependent particle interpretation generalises Gibbons' definition to non-stationary spacetimes. This allows any observer to be considered, providing a particle interpretation that depends {\it only} on the observer's motion and the background, not on any choice of coordinates or gauge, or on details of their particle detector. Consistency with known results is demonstrated for the cases of Rindler space and deSitter space. Radar time is also considered for an arbitrarily moving observer in an arbitrary 1+1 dimensional spacetime, and for a comoving observer in a 3+1 dimensional FRW universe with arbitrary scale factor $a(t)$. Finite volume measurements and their fluctuations are also discussed, allowing one to say with definable precision where and when the particles are observed.