English

A unified quantization of gravity and other fundamental forces of nature

General Relativity and Quantum Cosmology 2022-08-02 v3 High Energy Physics - Theory

Abstract

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 us\ann{as} abbreviate the spatial Hamilton functions of the Standard Model by HSMH_{SM} and the Hamilton function of gravity by HGH_G. Working in a fiber bundle EE with base space \socc=R[n]\socc=\R[n], where the fiber elements are Riemannian metrics, we can express the Hamilton functions in the form HG+HSM=HG+t23H~SMH_G+H_{SM}=H_G+t^{-\frac23}\tilde H_{SM} if n=3n=3, where H~SM\tilde H_{SM} depends on metrics \sij\s_{ij} satisfying det\sij=1\det{\s_{ij}}=1. In the quantization process, we quantize HGH_G for general \sij\s_{ij} but H~SM\tilde H_{SM} only for \sij=\deij\s_{ij}=\de_{ij} by the usual methods of QFT. Let vv \resp ψ\psi be the spatial eigendistributions of the respective Hamilton operators, then, the solutions uu of the Wheeler-DeWitt equation are given by u=wvψu=wv\psi, where ww satisfies an ODE and uu is evaluated at (t,\deij)(t,\de_{ij}) in the fibers.

Keywords

Cite

@article{arxiv.2206.11367,
  title  = {A unified quantization of gravity and other fundamental forces of nature},
  author = {Claus Gerhardt},
  journal= {arXiv preprint arXiv:2206.11367},
  year   = {2022}
}

Comments

32 pages, v3: This is the published version. arXiv admin note: text overlap with arXiv:1301.6101, arXiv:2104.08084