Quantum cosmological Friedman models with a massive Yang-Mills field

TL;DR

This paper establishes a spectral resolution for the Wheeler-DeWitt equation in quantum cosmology with a massive Yang-Mills field, advancing understanding of quantum gravitational models with non-trivial matter content.

Contribution

It introduces a method to solve the Wheeler-DeWitt equation by separating gravitational and Yang-Mills eigenvalue problems, highlighting the role of mass as an eigenvalue.

Findings

Spectral resolution of the Wheeler-DeWitt equation achieved.

Eigenvalue problem for Yang-Mills field solved with mass as eigenvalue.

Method applicable to quantum cosmological models with massive gauge fields.

Abstract

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a massive Yang-Mills field. The resolution is achieved by first solving the free eigenvalue problem for the gravitational field and then the constrained eigenvalue problem for the Yang-Mills field. In the latter case the mass of the Yang-Mills field assumes the role of the eigenvalue.