Nonperturbative aspects of Yang-Mills theory

TL;DR

This thesis explores nonperturbative features of Yang-Mills theory, including confinement, propagator behavior, and the impact of external charges, using Hamiltonian and variational methods across different gauges.

Contribution

It provides a comprehensive nonperturbative analysis of Yang-Mills theory's infrared and ultraviolet regimes, connecting Coulomb and Landau gauges and calculating propagators and potentials.

Findings

Linearly rising static Coulomb potential indicating confinement

Infrared diverging gluon energy signals confinement

Nonperturbative running coupling constant studied in ultraviolet

Abstract

In this thesis, several aspects of Yang-Mills theory are studied. It begins with the constrained quantization in the Coulomb gauge, using the Dirac bracket formalism. A nonperturbative analysis of the infrared asymptotics of propagators in any spatial dimension follows, and a connection to the Landau gauge is given. In the Coulomb gauge Hamiltonian approach, a linearly rising static color Coulomb potential is found, along with an infrared diverging gluon energy, both signaling confinement. The propagators and vertices in the entire momentum regime are calculated with the variational principle. In the ultraviolet, a nonperturbative running coupling constant is studied, and certain asymptotic forms of the propagators are postulated. Furthermore, the back reaction of the gauge sector to the inclusion of external charges is investigated.