Signals of Confinement in the Dyson-Schwinger Equation for the Gauge Boson Propagator

TL;DR

This thesis advances the understanding of confinement in Yang-Mills theory by solving Dyson-Schwinger equations across gauges, improving truncation methods, and proposing a gauge-independent criterion to distinguish phases.

Contribution

It introduces a self-consistent solution of coupled Dyson-Schwinger equations including sunset diagrams, develops a generalized confinement criterion, and explores gauge dependence in confinement scenarios.

Findings

Successful self-consistent solutions for gluon and ghost propagators.

Development of a gauge-independent confinement criterion.

Identification of unphysical contributions in the infrared limit.

Abstract

In the first part of this thesis a coupled truncated set of Dyson-Schwinger equations (DSEs) including the one for the gluon-propagator is solved self-consistently over the whole momentum range. In Landau gauge the truncation of the coupled set of DSEs for the ghost and gluon propagators is improved by the first full inclusion of the sunset diagram. A solution method which avoids all overlapping divergences is presented. In the Maximal Abelian gauge a truncation is developed with respectively one infrared and one ultraviolet leading diagram included. A first solution of the ghost equation is presented. In the second part generalizations of the Kugo-Ojima confinement scenario to other gauges than the linear covariant gauge are investigated. In the generalized covariant gauge no contradiction is found by using a Faddeev-Popov conjugation invariant assignment of the asymptotic fields. In the last section a gauge-independent generalized criterion is developed which allows for the identification of the Coulomb, Higgs- and confining phases of Yang-Mills theory in terms of the infrared limit of the Dyson-Schwinger equation of the gauge boson propagator. While in a Coulomb phase the photon is massless, dominating the infrared of the equation, in the Higgs phase this equation is dominated by the physical mass of the gauge boson. In the confining phase the equation is saturated by unphysical degrees of freedom in the infrared limit only. This proposal is tested in a variety of gauges and the corresponding unphysical terms are identified.