Finite element methods for low-dimensional fermion field theories

Abstract

We examine lattice fermion models based on operator difference equations derived using the method of finite elements, motivated by the absence of species doubling in such formulations. Interacting fermion theories in (0+1) and (1+1) spacetime dimensions are constructed, and shown to be consistent in the sense that suitably defined equal time commutation relations are preserved from timeslice to timeslice. Using weak coupling perturbation theory to calculate the two-point function, we show that the non-locality inherent in the differencing scheme results in a violation of microcasuality in the continuum limit.