Basis Function Calculations for the Massive Schwinger Model in the Light-Front Tamm-Dancoff Approximation

Abstract

We use light-front field theory to study the massive Schwinger model. After making a Tamm-Dancoff truncation of Fock space so that no more than four particles are allowed in any state, the coupled light-front Tamm-Dancoff integral equations for charge zero states are solved by expanding the two-particle and four-particle amplitudes in a finite basis, thereby converting the original equations into a simple matrix equation. By retaining the four-particle sector we are able to study both the lowest energy boson of the theory and the first excited state, which for massless fermions is a scattering state of two ground state bosons. Known results for the massless Schwinger model are accurately reproduced with reasonably small bases, and existing numerical results for the massive model are reproduced and improved. The rich physics of the Schwinger model is used to elucidate several simple problems in the use of basis functions to solve Hamiltonian field theories.