Analytic continuation and physical content of the gluon propagator

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 Kallen-Lehmann description. A simple toy model shows how the elementary eigenvalues might be related to actual physical quasiparticles of the nonperturbative vacuum.

Automated summary

The gluon propagator's analytic continuation is revised to consider the possible existence of complex conjugated poles. The anomalous pole's contribution must be added when Wick rotating, which results in an effective Minkowskian propagator not obtained by simply continuing the Euclidean function. The effective propagator is represented by an integral of a spectral function naturally related to elementary (complex) eigenvalues of the Hamiltonian, thereby generalizing the Kallen-Lehmann description. A simple toy model demonstrates how the elementary eigenvalues might correspond to physical quasiparticles in the nonperturbative vacuum.