Semi-classical quantization of the sine-Gordon model was done by Ludwig Faddeev and Vladimir Korepin. The exact quantum scattering matrix was discovered by Alexander Zamolodchikov. This model is S-dual to the Thirring model, as discovered by Coleman. This is sometimes known as the Coleman correspondence and serves as an example of boson-fermion correspondence in the interacting case. This article also showed that the constants appearing in the model behave nicely under renormalization : there are three parameters α α 0 , β β and γ γ 0 . Coleman showed α α 0 receives only a multiplicative correction, γ γ 0 receives only an additive correction, and β β is not renormalized. Further, for a critical, non-zero value β β = 4 π π , the theory is in fact dual to a free massive Dirac field theory.