# MathSciDoc: An Archive for Mathematician ∫

#### Mathematical PhysicsTheoretical Physicsmathscidoc: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
[ Download ] [ 2021-03-17 20:24:02 uploaded by gerhardt ] [ 756 downloads ] [ 0 comments ]
• This is the published version. Two sections, 2 and 8, have been added.
```@inproceedings{claus2021the,
title={The quantization of gravity: Quantization of the Hamilton equations},
author={Claus Gerhardt},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210317202402279844745},
booktitle={Universe},
volume={7},
number={4},
pages={91},
year={2021},
}
```
Claus Gerhardt. The quantization of gravity: Quantization of the Hamilton equations. 2021. Vol. 7. In Universe. pp.91. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210317202402279844745.
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