Reconstructing propagators of confined particles in the presence of complex singularities

Propagators of confined particles, especially the Landau-gauge gluon propagator, may have complex singularities as suggested by recent numerical works well several theoretical models, e.g., motivated Gribov problem. In this paper, we study formal aspects propagators with in reconstructing Minkowski starting from Euclidean analytic continuation. We derive following properties rigorously for arbitrary satisfying some boundedness condition. The two-point Schwinger function violates reflection positivity. presence singularities, while holomorphy usual tube is maintained, reconstructed Wightman on spacetime becomes a nontempered distribution and positivity On other hand, Lorentz symmetry locality are kept intact under reconstruction. Finally, argue that can be realized state space an indefinite metric correspond to states. also discuss consequences Becchi-Rouet-Stora-Tyutin formalism. Our results could open up new way understanding confinement mechanism, mainly Yang-Mills theory.