We consider a three-dimensional model of spinor fields with a Thirring-like, quadrilinear selfinteraction. Using either two-or four-component Dirac spinors, we prove that the 1 / N expansion for the model is renormalizable if a gauge structure to select physical quantities is introduced. For certain values of the coupling, the leading 1 / N approximation exhibits bound-state poles. Dynamical breaking of parity or chiral symmetry is shown to occur as a cooperative effect of different orders of 1 / N , if N is smaller than the critical value N,= 1 2 8 / r 2~, where D is two or four depending on whether the fermion field has two or four components.

No abstract

We show that the noncommutative Wess-Zumino model is renormalizable to all orders of perturbation theory. The noncommutative scalar potential by itself is non-renormalizable but the Yukawa terms demanded by supersymmetry improve the situation turning the theory into a renormalizable one. As in the commutative case, there are neither quadratic nor linear divergences.Hence, the IR/UV mixing does not give rise to quadratic infrared poles.

We study the exact equivalence between the self-dual model minimally coupled with a Dirac field and the Maxwell-Chern-Simons model with nonminimal magnetic coupling to fermions. We show that the fermion sectors of the models are equivalent only if a Thirring like interaction is included.Using functional methods we verify that, up to renormalizations, the equivalence persists at the quantum level.

We study some consequences of the introduction of a Lorentz-violating modification term in the linearized gravity, which leads to modified dispersion relations for gravitational waves in the vacuum. We also discuss possible mechanisms for the induction of such a term in the Lagrangian.