H. Bozkaya, A. Ivanov, M. Pitschmann:

"On renormalizability of the massless Thirring model";

Journal of Physics A: Mathematical and General,39(2006), 11075 - 11089.

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, parameterized by two parameters. The

region of variation of these parameters is constrained by the positive definiteness

of the norms of the wavefunctions 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

themassless Thirring model in the sense that the ultraviolet 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

wavefunction of the massless Thirring fermion fields only.

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