Non-perturbative singularity structure of gluon and quark propagators

A gauge invariant, non-local observable is constructed in lattice pure gaug e theory, which is identical to the gluon propagator ge in a particular gau ge. The transfer matrix formalism is used to show that this correlator deca ys exponentially with eigenvalues of the Hamiltonian. This implies a gauge invariant singularity structure of the propagator in momentum space, permit ting a nonperturbative definition of a parton mass. The relation to gauge f ixing and the extension to matter fields axe discussed. (C) 2001 Published by Elsevier Science B.V.