On renormalizability 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 expressions for the causal two–point Green function and correlation function of left–right fermion densities with dynamical dimensions of fermion fields, parameterised by two parameters. The region of variation of these parameters is constrained by the positive definiteness of the norms of the wave functions of the states related to components of the fermion vector current. We show that the dynamical dimensions of fermion fields calculated for causal Green functions and correlation functions of left–right fermion densities can be made equal. This implies the renormalizability 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, can be removed by renormalization of the wave function of the massless Thirring fermion fields only. PACS: 11.10.Gh, 11.10.Kk, 11.10.Lm, 11.30.Rd 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