The Schwinger model

The Schwinger model (quantum electrodynamics with massless fermions in two space-time dimensions) is investigated. The eigenenergies of the Dirac Hamiltonian are found to depend on the gauge field in a gauge invariant manner. Some of the eigenstates of the full quantum Hamiltonian are found in the Fock space of the free fermionic Hamiltonian. The bosonization of the model is presented and used to obtain the axial anomaly equation, the exact two-point Wightman functions, and the current correlation function. Other two dimensional theories are discussed with emphasis on the aspects which are similar to the Schwinger model.Science, Faculty ofPhysics and Astronomy, Department ofGraduat