Quantum models a la Gabor for space-time metric

TL;DR

This paper extends Gabor signal processing through covariant Weyl-Heisenberg integral quantization to transform space-time functions into operators, applying it to general relativity's metric field to produce regularized semi-classical portraits with modified energy densities.

Contribution

It introduces a novel quantization method for space-time metrics using covariant Weyl-Heisenberg integral, bridging signal processing and quantum gravity.

Findings

Generated regularized semi-classical phase space portraits of metrics

Applied method to Schwarzschild and accelerated frames

Discussed probabilistic aspects of the quantization process

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.