# Quantum models à la Gabor for 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}) 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.