Equivalence of the sine-Gordon and Thirring models and cumulative mass effects

Abstract

We investigate the equivalence of the sine-Gordon and Thirring models on the basis of the short-distance behavior in the massive Thirring model. We find that for $\mathrm{dim}\overline{\ensuremath{\psi}}\ensuremath{\psi}\ensuremath{\ge}1$ there is a new additive renormalization effect originating from the occurrence of nonleading mass singularities in the spinor vacuum expectation values. In the sine-Gordon language this effect makes its appearance as a "cumulative" mass effect. It leads to a breakdown of the naive variational method.