The quantization of gravity: Quantization of the Hamilton equations

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

Mathematical Physics Theoretical Physics mathscidoc:2103.22001

Universe, 7, (4), 91, 2021.4
We quantize the Hamilton equations instead of the Hamilton condition. The resulting equation has the simple form $-\D u=0$ in a fiber bundle, where the Laplacian is the Laplacian of the Wheeler-DeWitt metric provided $n\not=4$. Using then separation of variables the solutions $u$ can be expressed as products of temporal and spatial eigenfunctions, where the spatial eigenfunctions are eigenfunctions of the Laplacian in the symmetric space $SL(n,\R[])/SO(n)$. Since one can define a Schwartz space and tempered distributions in $SL(n,\R[])/SO(n)$ as well as a Fourier transform, Fourier quantization can be applied such that the spatial eigenfunctions are transformed to Dirac measures and the spatial Laplacian to a multiplication operator.
quantization of gravity, quantum gravity, quantization of the Hamilton equations, temporal and spatial eigenfunctions, Fourier quantization, symmetric spaces
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  • This is the published version. Two sections, 2 and 8, have been added.
  title={The quantization of gravity: Quantization of the Hamilton equations},
  author={Claus Gerhardt},
Claus Gerhardt. The quantization of gravity: Quantization of the Hamilton equations. 2021. Vol. 7. In Universe. pp.91.
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