Fermionic determinant of the massive Schwinger model

A representation for the fermionic determinant of the massive Schwinger model, or two-dimensional QED (${\mathrm{QED}}_2$), is obtained that makes a clean separation between the Schwinger model and its massive counterpart. From this it is shown that the index theorem for ${\mathrm{QED}}_2$ follows from gauge invariance, that the Schwinger model’s contribution to the determinant is canceled in the weak-field limit, and that the determinant vanishes when the field strength is sufficiently strong to form a zero-energy bound state.