Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-12-22
J.Phys.A39:11075-11090,2006
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, Latex, the contribution of fermions with opposite chirality is added,the parameterisation of fermion determinant by
Scientific paper
10.1088/0305-4470/39/35/009
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.
Bozkaya H.
Ivanov Andrei N.
Pitschmann Mario
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