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