Quantum sine-Gordon equation as the massive Thirring model

The sine-Gordon equation is the theory of a massless scalar field in one space and one time dimension with interaction density proportional to cosβφ, where β is a real parameter. I show that if β² exceeds 8π, the energy density of the theory is unbounded below; if β² equals 4π, the theory is equivalent to the zero-charge sector of the theory of a free massive Fermi field; for other values of β, the theory is equivalent to the zero-charge sector of the massive Thirring model. The sine-Gordon soliton is identified with the fundamental fermion of the Thirring model.