Reconstructing confined particles with complex singularities

Complex singularities have been suggested in propagators of confined particles, e.g., the Landau-gauge gluon propagator. We rigorously reconstruct Minkowski from Euclidean with complex singularities. As a result, analytically continued Wightman function is holomorphic tube, and Lorentz symmetry locality are kept intact, whereas reconstructed violates temperedness positivity condition. Moreover, we argue that correspond to zero-norm states an indefinite metric state space.