The quantization of gravity

Claus Gerhardt Ruprecht-Karls-Universität, Institut für Angewandte Mathematik

Mathematical Physics mathscidoc:1609.22008

Adv. Theor. Math. Phys., 22, (3), 709 - 757, 2018.10
In a former paper we proposed a model for the quantization of gravity by working in a bundle $E$ where we realized the Hamilton constraint as the Wheeler-DeWitt equation. However, the corresponding operator only acts in the fibers and not in the base space. Therefore, we now discard the Wheeler-DeWitt equation and express the Hamilton constraint differently, either with the help of the Hamilton equations or by employing a geometric evolution equation. There are two possible modifications possible which both are equivalent to the Hamilton constraint and which lead to two new models. In the first model we obtain a hyperbolic operator that acts in the fibers as well as in the base space and we can construct a symplectic vector space and a Weyl system. In the second model the resulting equation is a wave equation in $\so \times (0,\infty)$ valid in points $(x,t,\xi)$ in $E$ and we look for solutions for each fixed $\xi$. This set of equations contains as a special case the equation of a quantized cosmological Friedman universe without matter but with a cosmological constant, when we look for solutions which only depend on $t$. Moreover, in case $\so$ is compact we prove a spectral resolution of the equation.
unified field theory, quantization of gravity, quantum gravity, gravitational waves, graviton
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  title={The quantization of gravity},
  author={Claus Gerhardt},
  booktitle={Adv. Theor. Math. Phys.},
  pages={709 - 757},
Claus Gerhardt. The quantization of gravity. 2018. Vol. 22. In Adv. Theor. Math. Phys.. pp.709 - 757.
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