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

TL;DR

This paper critiques the standard quantum field theory in curved spacetime, proposing a new Hamiltonian formalism that reveals quantum-gravitational nonlocality and shows no particle creation in such settings, impacting cosmology and black hole physics.

Contribution

It introduces a Hamiltonian approach to quantum fields in curved spacetime that addresses foundational issues and demonstrates the absence of particle creation in these scenarios.

Findings

Conventional commutation relations do not hold in curved spacetime.

Quantum-gravitational nonlocality is a fundamental feature.

No particle creation occurs in free quantum fields in curved spacetime.

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.