Theory of particle detection in curved spacetimes

Abstract

The dynamics of a scalar quantum field on a curved background is studied by the $c$-number method of external potential problems. The general situation typical for particle creation by gravitational field is considered: The incoming state is prepared at some initial Cauchy hypersurface and the outcome is only detected at a part of some final one. Bases are found which lead to the minimal possible particle creation compatible with such a situation. If the partition of the final Cauchy hypersurface is due to Killing horizons, as in the black-hole evaporation calculation, then these bases are physical and coincide with those usually employed. Exact and general formulas for the density matrix and entropy of the produced particles are given. The same ideas and methods lead to "particle creation" in empty Minkowski spacetime. Such particles are interpreted as produced by the detection process. A criterion is proposed by means of which one can distinguish particles created by a gravitational field from particles of another origin. Finally, a definition of positive frequency is discussed which is (1) sufficiently local to be independent from the far-away topology of spacetime, (2) independent of any additional structure such as Killing vectors, etc., (3) going over to the usual definition for zero curvature, and (4) well suited to the field dynamics. Its consequences seem to be compatible with experiments on elementary particles (we analyze some typical experiments).