Abstract
A gauge invariant, non-local observable is constructed in lattice pure gauge theory, which is identical to the gluon propagator in a particular gauge. The transfer matrix formalism is used to show that this correlator decays exponentially with eigenvalues of the Hamiltonian. This implies a gauge invariant singularity structure of the propagator in momentum space, permitting a non-perturbative definition of a parton mass. The relation to gauge fixing and the extension to matter fields are discussed.
Highlights
The confinement problem of QCD consists of the dynamical relation between perturbative parton physics at short distances and non-perturbative hadron physics at large distances
This is essential in the context of finite temperature and density physics probed in experimental heavy ion collisions, where creation of a “deconfined” quark gluon plasma is expected, whose collective physical properties should be determined by parton dynamics
Physical information about the parton dynamics is carried by their singularity structure
Summary
The confinement problem of QCD consists of the dynamical relation between perturbative parton physics at short distances and non-perturbative hadron physics at large distances. The pole mass defined from the quark propagator is gauge independent and infrared finite to every finite order in perturbation theory [1]. For the extraction of quark masses gauge fixing can be circumvented by the methods of non-perturbative renormalization, which make use of manifestly gauge invariant quantities [9].
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