Consistency and Lorentz invariance in the massive Schwinger model

The massive Schwinger model can be formulated in a canonically consistent way in the axial gauge, by supplementing the naive action with a surface integral. It was first shown that canonical consistency guarantees another consistency: charge is conserved without being forced to vanish; this result resolves a long-standing controversy. It is also shown that the surface modification ensures inhomogeneous Lorentz invariance. But, since a nonzero background field necessarily breaks translation invariance, the inhomogeneous Lorentz invariance is shown to hold only for charge-zero sectors