Restoration of Well-Defined Charge and Chiral Charge and Correct Lorentz-Transformation Property in the Thirring and Pre-Schwinger Models
Klaiber's method developed to construct an operator solution to the Thirring model is improved by introducing free massless two-vector field in such a way that modified fusion fields satisfy the same commutation relations as free massless boson fields given by Nakanishi but spontaneous breakdowns of charge and chiral charge are evaded. It is shown that there exist spurion operators which do not carry anything except charge and chiral charge, vacuum expectation values of spurion operators vanish and multiple vacua are unphysical states. It is also shown that modified free massless fermion field, which is equivalent to original one, can be rewritten as an exponential function which is nothing but Nakanishi's solution to free massless Dirac equation apart from multiplicative spurion operator part. The formulation is immediately applied to obtain operator solution to the Thirring and pre-Schwinger models which possess among others standard Lorentz-transformation property.