A unified quantization of gravity and other fundamental forces of nature

TL;DR

This paper develops a quantum framework unifying gravity with the Standard Model forces by quantizing their Hamilton functions within a fiber bundle approach, leading to solutions of the Wheeler-DeWitt equation.

Contribution

It introduces a novel quantization method for gravity and Standard Model interactions within a fiber bundle formalism, enabling solutions to the Wheeler-DeWitt equation.

Findings

Quantization of gravity coupled with Yang-Mills and spinor fields.

Explicit solutions to the Wheeler-DeWitt equation in this framework.

A new approach to unify all four fundamental forces quantum mechanically.

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 $H_{SM}$ 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.