More about the massive Schwinger model

Abstract

The massive Schwinger model is quantum electrodynamics of a Dirac particle of mass m and charge e in 1 + 1 dimensions. It is known that the physics of the model depends on an arbitrary parameter independent of e and m, an angle, θ,| θ| ⩽ π. I give a physical explanation of this angle, and explain why a corresponding parameter does not appear in (3 + 1)-dimensional electrodynamics. I also compute some quantitative properties of the theory for both weak coupling, e ≪ m, and strong coupling, e ≫ m, and conjecture a qualitative description of the model that interpolates smoothly between weak and strong coupling. A typical quantitative result is that for weak coupling and | θ| ≠ π, the number of stable particles in the theory is 4 m 2 π e 2 1 ( 1 − θ 2 / π 2 ) [ 2 3 − In ( 2 + 3 ] + O ( 1 ) I do similar computations for a generalization of the model with “flavor SU(2), ” i.e., with two fermions of equal charge and mass. For weak coupling the results are very much like those for the massive Schwinger model, but for strong coupling there are some surprising differences.