Quantum Fields in Curved Spacetime: Quantum-Gravitational Nonlocality and Conservation of Particle Numbers

Abstract

We argue that the conventional quantum field theory in curved spacetime has a grave drawback: The canonical commutation relations for quantum fields and conjugate momenta do not hold. Thus the conventional theory should be denounced and the related results revised. A Hamiltonian version of the canonical formalism for a free scalar quantum field is advanced, and the fundamentals of an appropriate theory are constructed. The principal characteristic feature of the theory is quantum-gravitational nonlocality: The Schroedinger field operator at time t depends on the metric at t in the whole 3-space. Applications to cosmology and black holes are given, the results being in complete agreement with those of general relativity for particles in curved spacetime. A model of the universe is advanced, which is an extension of the Friedmann universe; it lifts the problem of missing dark matter. A fundamental and shocking result is the following: There is no particle creation in the case of a free quantum field in curved spacetime; in particular, neither the expanding universe nor black holes create particles.