Quantum Models à la Gabor for the Space-Time Metric

Abstract

As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space x,k into Hilbertian operators. The x=xμ values are space-time variables, and the k=kμ values are their conjugate frequency-wave vector variables. The procedure is first applied to the variables x,k and produces essentially canonically conjugate self-adjoint operators. It is next applied to the metric field gμν(x) of general relativity and yields regularized semi-classical phase space portraits gˇμν(x). The latter give rise to modified tensor energy density. Examples are given with the uniformly accelerated reference system and the Schwarzschild metric. Interesting probabilistic aspects are discussed.

Coherent states in quantum physics: an overview

“…In this contribution, we have just given a flavour of this variety through the works of the author and collaborators, specifically three of them which have recently been published. For other recent ones, with applications in different domains (quantum optics, cosmology, curved manifolds, signal analysis...) see [19,20,21,22,23].…”

Scientific Cosmogony, the Time in Quantum Relativistic Physics

“…calls scintillation events 5 , namely events each consisting in the virtual creation of a particle-antiparticle pair, followed, a short time later, by its annihilation. If the particles of the pair are fermions, such event would contribute to a negative curvature (normal de Sitter) world matter, a sort of a baryonic Fermi-Dirac Sea, at the exterior of the Hubble horizon, and if they are bosons, the event would contribute to a positive curvature (anti-de Sitter) world matter, a gluonic Bose-Einstein condensate, at the interior of the Hubble horizon.…”

“…This kinematical time operator has an informational content within the framework of signal analysis. It is canonically conjugate to the frequency operator and no Planck constant h is involved here (see [4] and [5] for details). Now, it turns out that rather recently, important encouraging events occurred in the domain of a possible reconciliation of quantum physics and general relativity.…”