Thirring Model - Definition

Definition

The Thirring model is given by the Lagrangian density

$\mathcal{L}= \overline{\psi}(i\partial\!\!\!/-m)\psi -\frac{g}{2}\left(\overline{\psi}\gamma^\mu\psi\right) \left(\overline{\psi}\gamma_\mu \psi\right)\$

where is the field, g is the coupling constant, m is the mass, and, for, are the two-dimensional gamma matrices.

This is the unique model of (1+1)-dimensional, Dirac fermions with a local (self-)interaction. Indeed, since there are only 4 independent fields, because of the Pauli principle, all the quartic, local interactions are equivalent; and all higher power, local interactions vanish. (Interactions containing derivatives, such as $(\bar \psi\partial\!\!\!/\psi)^2$ , are not considered because they are non-renormalizable.)

The correlation functions of the Thirring model (massive or massless) verify the Osterwalder-Schrader axioms, and hence the theory makes sense as a quantum field theory.

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