Quantum Models à la Gabor for the Space-Time Metric

As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space [Formula: see text] into Hilbertian operators. The [Formula: see text] values are space-time variables, and the [Formula: see text] values are their conjugate frequency-wave vector variables. The procedure is first applied to the variables [Formula: see text] and produces essentially canonically conjugate self-adjoint operators. It is next applied to the metric field [Formula: see text] of general relativity and yields regularized semi-classical phase space portraits [Formula: see text]. 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.