Quantum models a la Gabor for space-time metric
| Autor: | Cohen-Tannoudji, Gilles, Gazeau, Jean-Pierre, Habonimana, Célestin, Shabani, Juma |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Entropy 2022, 24(6), 835 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3390/e24060835 |
| Popis: | 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. Comment: 22 pages |
| Databáze: | arXiv |
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