The Schwinger point

The Sommerfield model with a massive vector field coupled to a massless fermion in 1+1 dimensions is an exactly solvable analog of a Bank-Zaks model. The “physics” of the model comprises a massive boson and an unparticle sector that survives at low energy as a conformal field theory (Thirring model). I discuss the “Schwinger point” of the Sommerfield model in which the vector boson mass goes to zero. The limit is singular but gauge invariant quantities should be well-defined. I give a number of examples, both (trivially) with local operators and with nonlocal products connected by Wilson lines (the primary technical accomplishment in this note is the explicit and very pedestrian calculation of correlators involving straight Wilson lines). I hope that this may give some insight into the nature of bosonization in the Schwinger model and its connection with unparticle physics which in this simple case may be thought of as “incomplete bosonization.”