Hamiltonian treatment of the (2+1)-dimensional Yang-Mills theory

The (2+l)-dimensional Yang-Mills theory is studied in the functional Schrödinger formalism using the machinery laid out by Karabali and Nair. The low-lying spectrum of the theory is computed by analyzing correlators of the Leigh-Minic-Yelnikov ground-state wave-functional in the Abelian limit. The contribution of the WZW measure is treated by a controlled approximation and the resulting spectrum is shown to reduce to that obtained by Leigh et al., at large momentum. The inclusion of fundamental Fermions is done from first-principles, and it is found that the requirement of gauge invariance spoils the commutativity between gauge and matter fields.Science, Faculty ofPhysics and Astronomy, Department ofGraduat