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.

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.

The Nambu-Jona-Lasinio (NJL) model is one of the most frequently used four-fermion models in the study of dynamical symmetry breaking. In particular, the NJL model is convenient for that analysis at finite temperature, chemical potential and size effects, as has been explored in the last decade. With this motivation, we investigate the finite-size effects on the phase structure of the NJL model in D = 3 Euclidean dimensions, in the situations that one, two and three dimensions are compactified. In this context, we employ the zeta-function and compactification methods to calculate the effective potential and gap equation. The critical lines that separate trivial and non-trivial fermion mass phases in a second order transition are obtained. We also analyze the system at finite temperature, considering the inverse of temperature as the size of one of the compactified dimensions.The last decades witnessed significant investigations on the phase structure of quantum field theories, in particular on the chiral symmetry phase transitions in Quantum Cromodynamics (QCD). However, due to its complex structure, effective models have been largely employed to simplify that analysis. Among them, one of the most frequently used is the four-fermion theory known as Nambu-Jona-Lasinio (NJL) model [1]. The NJL model is specially convenient for the investigation of dynamical symmetries when the system is under certain conditions, like finite temperature, finite chemical potential, external gauge field, gravitation field and others [2,3,4].Finite-size effects on the phase transitions of four-fermion models have also attracted a great interest [5,6,7]. This question emerges when the system has a finite size and it is not clear if it is large enough to apply the thermodynamic limit in a usual way; frequently it is necessary to take into account the fluctuations due to finite-size effects. In particular, Ref.[6] performed a numerical investigation of a three-dimensional four-fermion model in a finite-size scaling analysis, where the finite-size effects act as an external field. On the other hand, Ref.[7] studied the NJL model in the framework of the multiple reflection expansion, where in terms of a modified density of states finite-size effects are included (see also Ref. [8]). The critical temperature was suggested to decrease as the system is reduced.In this paper, we investigate finite-size effects on the dynamical symmetry breaking in a different way. We study the Euclidean three-dimensional NJL model in the framework of zeta-function and compactification methods [9]. This procedure in principle allows us to explore the mentioned model with one, two or three compactified dimensions with antiperiodic boundary conditions [17] and compare their effects in the phase diagram of the model. With the choice of all dimensions being spatial, the system is considered confined between two parallel planes a distance L apart, confined to a infinity cylinder having a square transversal section of area L 2 , and to a cubic box of volume L 3 , for ...

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The three-dimensional noncommutative supersymmetric QED is investigated within the superfield approach. We prove the absence of UV/IR mixing in the theory at any loop order and demonstrate its one-loop finiteness.  2003 Published by Elsevier B.V.During last years noncommutative gauge theories have been intensively studied. The interest in this subject has deep motivations coming mainly from string theory [1] (for a review see [2,3]). Different aspects of noncommutative gauge theories were discussed in [4][5][6][7][8][9][10][11].One of the most remarkable properties of noncommutative theories consists of an unusual structure of divergences, the so-called UV/IR mixing, that could lead to the appearance of infrared divergences [4,12]. It should be noticed that the cancellation of quadratic and linear ultraviolet divergences in commutative theories does not guarantee the absence of harmful infrared divergences in their noncommutative counterparts [13][14][15][16]. The elimination of such divergences is crucial since they may obstruct the development of a sound renormalization scheme, leading to the breakdown of the perturbative series.Based on experience, it is natural to expect that supersymmetry could improve this situation [4,17]. In fact, the Wess-Zumino model [14] and the three-dimensional sigma-model [18] are renormalizable at all loop orders. This is furtherly supported by the results of [19] according to which the one-loop effective action in N = 1, 2 super-Yang-Mills theory contains only logarithmic divergences while for N = 4 the theory is one-loop finite [19,20].