Quantum Models à la Gabor for the Space-Time Metric

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.