Nonperturbative aspects of Yang-Mills theory

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.