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In order to better understand what to expect from numerical CORE computationsfor two-dimensional massless QED (the Schwinger model) we wish to obtain someanalytic control over the approach to the continuum limit for various choicesof fermion derivative. To this end we study the Hamiltonian formulation of thelattice Schwinger model (i.e., the theory defined on the spatial lattice withcontinuous time) in $A_0=0$ gauge. We begin with a discussion of the solutionof the Hamilton equations of motion in the continuum, we then parallel thederivation of the continuum solution within the lattice framework for a rangeof fermion derivatives. The equations of motion for the Fourier transform ofthe lattice charge density operator show explicitly why it is a regulatedversion of this operator which corresponds to the point-split operator of thecontinuum theory and the sense in which the regulated lattice operator can betreated as a Bose field. The same formulas explicitly exhibit operators whosematrix elements measure the lack of approach to the continuum physics. We showthat both chirality violating Wilson-type and chirality preserving SLAC-typederivatives correctly reproduce the continuum theory and show that there is aclear connection between the strong and weak coupling limits of a theory basedupon a generalized SLAC-type derivative.Comment: 27 pages, 3 figures, revte

Lattice Schwinger model: Confinement, anomalies, chiral fermions, and all that