1998/06/20 by Vladimir S. Mashkevich, Mashkevich, Vladimir S.
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.gr-qc/9806083
17 pages, no figures, LATEX 2.09
arxiv created 1998/06/20 · openalex publication_date 1998/06/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.