Classical and Quantum Fields in Curved Spacetime: Canonical Theory versus Conventional Construction

Abstract

We argue that the conventional construction for quantum fields in curved spacetime has a grave drawback: It involves an uncountable set of physical field systems which are nonequivalent with respect to the Bogolubov transformations, and there is, in general, no canonical way for choosing a single system. Thus the construction does not result in a definite theory. The problem of ambiguity pertains equally both to quantum and classical fields. The canonical theory is advanced, which is based on a canonical, or natural choice of field modes. The principal characteristic feature of the theory is relativistic-gravitational nonlocality: The field at a spacetime point $(s,t)$ depends on the metric at $t$ in the whole 3-space. The most fundamental and shocking result is the following: In the case of a free field in curved spacetime, there is no particle creation. Applications to cosmology and black holes are given. The results for particle energies are in complete agreement with those of general relativity. A model of the universe is advanced, which is an extension of the Friedmann universe; it lifts the problem of missing dark matter.