Abstract
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.
Highlights
Color confinement, the absence of colored degrees of freedom from the physical spectrum, is an essential element of strong interactions
In old literature [23,24,25,26,27,28], e.g., for models motivated by the Gribov ambiguity, it was predicted that the gluon propagator in the Landau gauge has a pair of complex poles, which is a typical example of such singularities
We prove the nontemperedness of (C) as follows: Suppose the Wightman function were tempered, the holomorphy in the tube would essentially imply the spectral condition for the Wightman function in momentum representation
Summary
The absence of colored degrees of freedom from the physical spectrum, is an essential element of strong interactions Understanding this fact in the framework of relativistic quantum field theory (QFT) is a fundamental issue of particle and nuclear physics. To investigate such fundamental aspects of strong interactions, the gluon, ghost, and quark propagators in the Landau gauge have been extensively studied by both lattice and continuum methods [1,2,3]. We provide full details of their rigorous proofs and derivations in a longer version [38]
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