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

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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 [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.