Quantum models a la Gabor for space-time metric

• URL: http://arxiv.org/abs/2205.11254v2
• Date: Tue, 21 Jun 2022 08:36:44 GMT
• Title: Quantum models a la Gabor for space-time metric
• Authors: Gilles Cohen-Tannoudji, Jean-Pierre Gazeau, C\'elestin Habonimana, and Juma Shabani
• Abstract summary: Weyl-Heisenberg integral quantization is implemented to transform functions on phase space $left(x,kright)$ into Hilbertian operators. The procedure is first applied to the variables $left(x,kright)$ and produces canonically conjugate essentially self-adjoint operators. It is next applied to the metric field $g_munu(x)$ of general relativity and yields regularised semi-classical phase space portraits.
• Score: 0.3149883354098941
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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 $\left(x,k\right)$ into Hilbertian operators. The $x=\left(x^{\mu}\right)$'s are space-time variables and the $k=\left(k^{\mu}\right)$'s are As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space $\left(x,k\right)$ into Hilbertian operators. The $x=\left(x^{\mu}\right)$'s are space-time variables and the $k=\left(k^{\mu}\right)$'s are their conjugate wave vector-frequency variables. The procedure is first applied to the variables $\left(x,k\right)$ 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 $\check{g}_{\mu\nu}(x)$. 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.

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