Quantum cosmological Friedman models with a Yang-Mills field and positive energy levels

TL;DR

This paper proves the existence of a spectral resolution for the Wheeler-DeWitt equation in quantum cosmology models with a Yang-Mills field, showing that the energy levels are strictly positive, which advances understanding of quantum gravitational systems.

Contribution

It establishes the spectral resolution of the Wheeler-DeWitt equation for models with Yang-Mills matter fields and positive energy levels in a homothetic spatial geometry.

Findings

Spectral resolution of the Wheeler-DeWitt equation is proven.

Eigenvalues (energy levels) are strictly positive.

Results apply to models with or without a mass term in the Yang-Mills field.

Abstract

We prove the existence of a spectral resolution of the Wheeler-DeWitt equation when the matter field is provided by a Yang-Mills field, with or without mass term, if the spatial geometry of the underlying spacetime is homothetic to $\R[3]$. The energy levels of the resulting quantum model, i.e., the eigenvalues of the corresponding self-adjoint Hamiltonian with a pure point spectrum, are strictly positive.