Quantum Cosmology with Yang-Mills Fields

TL;DR

This paper extends quantum cosmology models to include Yang-Mills fields, deriving the wave function for an $SO(3)$ gauge group and analyzing inhomogeneous perturbations in a minisuperspace setting.

Contribution

It introduces a formalism for incorporating Yang-Mills fields into quantum cosmology, specifically expanding in harmonics on three-spheres and deriving the semi-classical wave function for $SO(3)$ gauge fields.

Findings

Derived explicit formulas for $SO(N)$ gauge fields in quantum cosmology.

Obtained the Lagrangian and semi-classical wave function for $SO(3)$ gauge group.

Analyzed inhomogeneous perturbations around a homogeneous background.

Abstract

We examine an extension of the ideas of quantum cosmology and, in particular, the proposal of Hartle and Hawking for the boundary conditions of the Universe, to models which incorporate Yang-Mills fields. Inhomogeneous perturbations about a homogeneous, isotropic minisuperspace background model are considered, by expanding the Yang-Mills fields in harmonics of the spatial directions which are taken to be three-spheres. The expansions are made explicit for $SO(N)$ gauge fields thereby obtaining formulae compatible with the formalism conventionally used in quantum cosmology. We apply these results to the gauge group $SO(3)$ and derive the Lagrangian and the semi-classical wave function for this special case.