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Quantum Models à la Gabor for the Space-Time Metric.

Gilles Cohen-Tannoudji1, Jean-Pierre Gazeau2, Célestin Habonimana3

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Summary
This summary is machine-generated.

Covariant Weyl-Heisenberg integral quantization transforms phase space functions into operators. This method modifies general relativity

Keywords:
covariant Weyl-Heisenberg integral quantizationgeneral relativitygeometry of informationposition-wave vectorspace-time metrictime-frequency

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Area of Science:

  • Quantum mechanics
  • General relativity
  • Signal processing

Background:

  • Gabor signal processing provides a foundation.
  • Phase space representations are crucial in physics.
  • Canonical quantization is a standard technique.

Purpose of the Study:

  • To implement covariant Weyl-Heisenberg integral quantization.
  • To apply this to spacetime variables and the metric field.
  • To explore resulting modifications in general relativity.

Main Methods:

  • Integral quantization based on Weyl-Heisenberg framework.
  • Application to 8D phase space (x, k).
  • Quantization of the metric field gμν(x).

Main Results:

  • Generation of canonically conjugate self-adjoint operators.
  • Regularized semi-classical phase space portraits (gˇμν(x)).
  • Modified tensor energy density derived from these portraits.

Conclusions:

  • The method offers a novel approach to quantizing fields.
  • It provides insights into quantum gravity and spacetime structure.
  • Probabilistic interpretations are discussed for physical systems.