Burden, Conrad J.Roberts, Craig D.Williams, Anthony G.2026-01-022026-01-020370-2693ORCID:/0000-0003-0015-319X/work/167650888https://hdl.handle.net/1885/733802816A model Schwinger-Dyson equation for the fermion self-energy is solved for both spacelike and timelike momenta. The singularity structure of the quark propagator obtained as a solution of this equation is studied. It is found to be an entire function (except for an essential singularity at p2 = -∞; timelike in our metric): a property that may be indicative of confinement. The absence of singularities is a non-trivial feature that arises only as a result of the cancellation of zeros in the numerator and denominator of the propagator.We are grateful to H. Munczek for comments made in connection with an early draft of this manuscript. The work of C.D.R. was supported by the Department of Energy, Nuclear Physics Division, under contract number W-31-109-ENG-38. The work of A.G.W. was supported by the Department of Energy through Contract No. DE-FG05-86ER40273 and by the Florida State University Supercomputer Computations Research Institute which is partially funded by the Department of Energy through Contract No. DE-FC05-85ER250000.7en1992-07-1610.1016/0370-2693(92)91516-C0001325519