A unified quantization of gravity and other fundamental forces of nature

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

Mathematical Physics Theoretical Physics mathscidoc:2206.22008

Universe, 8, (8), 404, 2022.8
We quantize the interaction of gravity with Yang-Mills and spinor fields, hence offering a quantum theory incorporating all four fundamental forces of nature. Let as abbreviate the spatial Hamilton functions of the Standard Model by $H_{SM}$ and the Hamilton function of gravity by $H_G$. Working in a fiber bundle $E$ with base space $\socc=\R[n]$, where the fiber elements are Riemannian metrics, we can express the Hamilton functions in the form $H_G+H_{SM}=H_G+t^{-\frac23}\tilde H_{SM}$ if $n=3$, where $\tilde H_{SM}$ depends on metrics $\s_{ij}$ satisfying $\det{\s_{ij}}=1$. In the quantization process, we quantize $H_G$ for general $\s_{ij}$ but $\tilde H_{SM}$ only for $\s_{ij}=\de_{ij}$ by the usual methods of QFT. Let $v$ \resp $\psi$ be the spatial eigendistributions of the respective Hamilton operators, then, the solutions $u$ of the Wheeler-DeWitt equation are given by $u=wv\psi$, where $w$ satisfies an ODE and $u$ is evaluated at $(t,\de_{ij})$ in the fibers.
quantum gravity, Yang-Mills field, spinor field, Standard Model, unification, unified quantum theory
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@inproceedings{claus2022a,
  title={A unified quantization of gravity and other fundamental forces of nature},
  author={Claus Gerhardt},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220618194457466644418},
  booktitle={Universe},
  volume={8},
  number={8},
  pages={404},
  year={2022},
}
Claus Gerhardt. A unified quantization of gravity and other fundamental forces of nature. 2022. Vol. 8. In Universe. pp.404. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220618194457466644418.
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