A unified quantum theory II: gravity interacting with Yang-Mills and spinor fields

TL;DR

This paper develops a quantum theory unifying gravity with Yang-Mills and spinor fields, using canonical quantization, solutions to the Wheeler-DeWitt equation, and algebraic quantum field theory methods.

Contribution

It introduces a comprehensive quantum framework for gravity interacting with gauge and matter fields, including solutions and algebraic structures respecting gauge and geometric symmetries.

Findings

Solutions to the Wheeler-DeWitt equation in a vector bundle

Construction of CCR and CAR representations for bosonic and fermionic fields

Definition of a local algebra net satisfying Haag-Kastler axioms

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. Using canonical quantization we obtain solutions of the Wheeler-DeWitt equation in a vector bundle and the method of second quantization leads to a symplectic vector space $(V,\om)$ and a corresponding CCR representation for the bosonic components and a CAR representation for the fermionic part. The solution space of the Wheeler-DeWitt equation is invariant under gauge transformations and under isometries in the spacelike base space $\so$ of a given Riemannian metric $\rho_{ij}$. We also define a net of local subalgebras which satisfy four of the Haag-Kastler axioms.