Nonperturbative many-body techniques applied to a Yang-Mills field theory

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Abstract
Starting from the cutoff version of a field-theoretical Hamiltonian derived from an SU(n) Yang-Mills theory in the Coulomb gauge, we investigate the structure of the emerging many-body problem within a Bogoliubov approximation for the ground state (= physical vacuum) and by considering suitable quasiparticle excitations for glueball states. The idea of the formation of a bag can be incorporated into this scheme. The energy expectation values are approximated by a cluster expansion. The (formal) results, allowing the numerical computation of the glueball spectrum at a later stage, are presented and the emerging structure is discussed. Special attention is hereby paid to the significance of the Gribov ambiguity and to the consequences of the singularity of the Hamiltonian at the Gribov horizon. It is suggested that the possibility of a rising potential between gluons be investigated, as such a potential could be a signal of confinement.