Analytic continuation and physical content of the gluon propagator

TL;DR

This paper revises the analytic continuation of the gluon propagator, highlighting the importance of complex conjugated poles and their impact on the Minkowskian form, with implications for understanding non-perturbative QCD.

Contribution

It introduces a modified analytic continuation framework for the gluon propagator that accounts for anomalous poles and relates the spectral function to complex eigenvalues of the Hamiltonian.

Findings

Effective Minkowskian propagator includes anomalous pole contributions.

Spectral function relates to complex eigenvalues, generalizing K"allen-Lehmann.

Toy model suggests connection between eigenvalues and physical quasiparticles.

Abstract

The analytic continuation of the gluon propagator is revised in the light of recent findings on the possible existence of complex conjugated poles. The contribution of the anomalous pole must be added when Wick rotating, leading to an effective Minkowskian propagator which is not given by the trivial analytic continuation of the Euclidean function. The effective propagator has an integral representation in terms of a spectral function which is naturally related to a set of elementary (complex) eigenvalues of the Hamiltonian, thus generalizing the usual K\"allen-Lehmann description. A simple toy model shows how the elementary eigenvalues might be related to actual physical quasiparticles of the non-perturbative vacuum.