On unrenormalizability of the massless Thirring model

We discuss the renormalizability of the massless Thirring model in terms of the causal fermion Green functions and correlation functions of left—right fermion densities. We obtain the most general solution of the massless Thirring model with dynamical dimensions of fermion fields, parameterized by two arbitrary parameters. We show that in the massless Thirring model there are no solutions which should provide equal dynamical dimensions for fermion fields calculated for causal Green functions and correlation functions of left–right fermion densities. This implies the unrenormalizability of the massless Thirring model in the sense that the ultra–violet cut–off dependence, appearing in the causal fermion Green functions and correlation functions of left–right fermion densities, cannot be removed by renormalization of the wave function of the massless Thirring fermion fields only. E–mail: [email protected], Tel.: +43–1–58801–14262, Fax: +43–1–58801–14299 E–mail: [email protected], Tel.: +43–1–58801–14261, Fax: +43–1–58801–14299 Permanent Address: State Polytechnic University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation E–mail: [email protected], Tel.: +43–1–58801–14263, Fax: +43–1–58801–14299 1