Reconstructing confined particles with complex singularities

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.

arXiv comment7 pages, 2 figures, final version published in PRD; a longer version can be found at arXiv:2105.07487 [hep-th]

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• Spectral Functions of Gauge Theories with Banks-Zaks Fixed Points
• Lattice pure gauge compact QED in the Landau gauge: the photon propagator, the phase structure and the presence of Dirac strings
• The analytic structure of the Landau gauge quark propagator from Padé analysis
• The analytic structure of three-point functions from contour deformations
• On the complex structure of Yang-Mills theory
• Resurgent Analysis of Ward-Schwinger-Dyson Equations
• The Nielsen identities in screened theories
• The Schwinger function, confinement and positivity violation in pure gauge QED
• Analytic continuation and physical content of the gluon propagator
• Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
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• $B\to X_c\ell \bar{\nu }$ Decay as a Probe of Complex Conjugate Poles
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