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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=(x^{\mu}) are space-time
variables and the k=(k^{\mu}) are their conjugate wave vector-frequency variables.
The procedure is first applied to the variables (x,k) and produces canonically
conjugate essentially self-adjoint operators. It is next applied to the metric
field g_{\mu\nu}(x) of general relativity and yields regularised semi-classical
phase space portraits of it. 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. |
