Upper bound on the color-confining potential

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Abstract
Under rather general assumptions it is shown that the (suitably defined) potential between color charges cannot rise faster than linearly with distance. The main ingredients are the existence of a positive Hamiltonian and invariance under 90° Euclidean rotations. In order to be on firm ground mathematically, the discussion is carried out for lattice theories; the role of the lattice, however, is purely technical.