On the equivalence between sine-Gordon model and Thirring model in the chirally broken phase of the Thirring model

We investigate the equivalence between Thirring model and sine-Gordon model in the chirally broken phase of the Thirring model. This is unlike all oth er available approaches where the fermion fields of the Thirring model were quantized in the chiral symmetric phase. In the path integral approach we show that the bosonized version of the massless Thirring model is described by a quantum field theory of a massless scalar field and exactly solvable, and the massive Thirring model bosonizes to the sine-Gordon model with a n ew relation between the coupling constants. We show that the non-perturbati ve vacuum of the chirally broken phase in the massless Thirring model can b e described in complete analogy with the BCS ground state of superconductiv ity. The Mermin-Wagner theorem and Coleman's statement concerning the absen ce of Goldstone bosons in the 1 + 1-dimensional quantum field theories are discussed. We investigate the current algebra in the massless Thirring mode l and give a new value of the Schwinger term. We show that the topological current in the sine-Gordon model coincides with the Noether current respons ible for the conservation of the fermion number in the Thirring model. This allows one to identify the topological charge in the sine-Gordon model wit h the fermion number.