Quantum Models a 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 x,k into Hilbertian operators. The x=x mu values are space-time variables, and the k=k mu 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 g mu nu(x) of general relativity and yields regularized semi-classical phase space portraits g7;mu nu(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.