Finite lattice fermions and gauge fields in 1+1 dimensions

New finite-lattice study of the massive Schwinger model

“…The limit of the sequence can again be estimated using the VBS routine. For the massless case, m/g = 0, this procedure works extremely well, as discovered by Irving and Thomas [13], and shown in Table II. For m/g = 0, we find by this procedure…”

“…The series can be reliably extrapolated to the continuum limit, and give detailed and accurate information about the spectrum, although not quite as accurate as the finite-lattice method presented in this paper. Finitelattice Hamiltonian calculations were performed by Crewther and Hamer [12] and Irving and Thomas [13] over fifteen years ago. Hamer et al [11] did some new finite-lattice calculations, but used free boundary conditions; here we use periodic boundary conditions, which should give better convergence.…”

Series expansions for the massive Schwinger model in Hamiltonian lattice theory

“…The leading term O((g/m) 1/3 ) has the correct behaviour as predicted by (14). The series have been calculated forf l (l = 0, 1, · · · , 6) up to order u 14 for the vector excited state and order u 13 for the scalar excited state.…”

“…The advantage would be that the finite-lattice corrections should be much smaller, and the finitelattice sequence should converge more rapidly. With today's computers, one could probably expect to obtain virtually exact eigenvalues on lattices up to some 20 sites, and thus obtain a substantial improvement on previous finite-lattice calculations [13,14].…”

“…A quite accurate variational calculation in the infinite momentum frame was performed by Bergknoff [12]. Finite-lattice Hamiltonian calculation were performed by Crewther and Hamer [13] and Irving and Thomas [14]: we include some further finite-lattice calculations in this paper, mainly as a check on the series results. Later on Eller, Pauli and Brodsky [15] applied a "discrete light-cone quantization" (DLCQ) approach to the problem, and showed that it gave quite good results, not only for the lowest state, but for a whole range of higher excited states.…”