The Low Energy Limit of the Chern-Simons Theory Coupled to Fermions

We study the nonrelativistic limit of the theory of a quantum Chern--Simons field minimally coupled to Dirac fermions. To get the nonrelativistic effective Lagrangian one has to incorporate vacuum polarization and anomalous magnetic moment effects. Besides that, an unsuspected quartic fermionic interaction may also be induced. As a by product, the method we use to calculate loop diagrams, separating low and high loop momenta contributions, allows to identify how a quantum nonrelativistic theory nests in a relativistic one.Comment: 18 pages, 8 figures, Late

Chiral Bosons Through Linear Constraints

We study in detail the quantization of a model which apparently describes chiral bosons. The model is based on the idea that the chiral condition could be implemented through a linear constraint. We show that the space of states is of indefinite metric. We cure this disease by introducing ghost fields in such a way that a BRST symmetry is generated. A quartet algebra is seen to emerge. The quartet mechanism, then, forces all physical states, but the vacuum, to have zero norm.Comment: 9 page

Chiral bosons and improper constraints

We argue that a consistent quantization of the Floreanini-Jackiw model, as a constrained system, should start by recognizing the improper nature of the constraints. Then each boundary conditon defines a problem which must be treated sparately. The model is settled on a compact domain which allows for a discrete formulation of the dynamics; thus, avoiding the mixing of local with collective coordinates. For periodic boundary conditions the model turns out to be a gauge theory whose gauge invariant sector contains only chiral excitations. For antiperiodoc boundary conditions, the mode is a second-class theory where the excitations are also chiral. In both cases, the equal-time algebra of the quantum energy-momentum densities is a Virasoro algebra. The Poincar\'e symmetry holds for the finite as well as for the infinite domain.Comment: 13 pages, Revtex file, IF.UFRGS Preprin

Rigorous Asymptotics of a KdV Soliton Gas

We analytically study the long time and large space asymptotics of a new broad class of solutions of the KdV equation introduced by Dyachenko, Zakharov, and Zakharov. These solutions are characterized by a Riemann–Hilbert problem which we show arises as the limit N→ + ∞ of a gas of N-solitons. We show that this gas of solitons in the limit N→ ∞ is slowly approaching a cnoidal wave solution for x→ - ∞ up to terms of order O(1 / x) , while approaching zero exponentially fast for x→ + ∞. We establish an asymptotic description of the gas of solitons for large times that is valid over the entire spatial domain, in terms of Jacobi elliptic functions

Nonrelativistic Limit of the Scalar Chern-Simons Theory and the Aharonov-Bohm Scattering

We study the nonrelativistic limit of the quantum theory of a Chern-Simons field minimally coupled to a scalar field with quartic self-interaction. The renormalization of the relativistic model, in the Coulomb gauge, is discussed. We employ a procedure to calculate scattering amplitudes for low momenta that generates their $|p|/m$ expansion and separates the contributions coming from high and low energy intermediary states. The two body scattering amplitude is calculated up to order $p^2/m^2$. It is shown that the existence of a critical value of the self-interaction parameter for which the 2-particle scattering amplitude reduces to the Aharonov-Bohm one is a strictly nonrelativistic feature. The subdominant terms correspond to relativistic corrections to the Aharonov-Bohm scattering. A nonrelativistic reduction scheme and an effective nonrelativistic Lagrangian to account for the relativistic corrections are proposed.Comment: 22 pages, 8 figures, revtex, to be published in Int. J. Mod. Phys.

Superfield covariant analysis of the divergence structure of noncommutative supersymmetric QED4_4

Commutative supersymmetric Yang-Mills is known to be renormalizable for ${\cal N} = 1, 2$, while finite for ${\cal N} = 4$. However, in the noncommutative version of the model (NCSQED$_4$) the UV/IR mechanism gives rise to infrared divergences which may spoil the perturbative expansion. In this work we pursue the study of the consistency of NCSQED$_4$ by working systematically within the covariant superfield formulation. In the Landau gauge, it has already been shown for ${\cal N} = 1$ that the gauge field two-point function is free of harmful UV/IR infrared singularities, in the one-loop approximation. Here we show that this result holds without restrictions on the number of allowed supersymmetries and for any arbitrary covariant gauge. We also investigate the divergence structure of the gauge field three-point function in the one-loop approximation. It is first proved that the cancellation of the leading UV/IR infrared divergences is a gauge invariant statement. Surprisingly, we have also found that there exist subleading harmful UV/IR infrared singularities whose cancellation only takes place in a particular covariant gauge. Thus, we conclude that these last mentioned singularities are in the gauge sector and, therefore, do not jeopardize the perturbative expansion and/or the renormalization of the theory.Comment: 36 pages, 11 figures. Minor correction

The coupling of fermions to the three-dimensional noncommutative CPN−1CP^{N-1} model: minimal and supersymmetric extensions

We consider the coupling of fermions to the three-dimensional noncommutative $CP^{N-1}$ model. In the case of minimal coupling, although the infrared behavior of the gauge sector is improved, there are dangerous (quadratic) infrared divergences in the corrections to the two point vertex function of the scalar field. However, using superfield techniques we prove that the supersymmetric version of this model with ``antisymmetrized'' coupling of the Lagrange multiplier field is renormalizable up to the first order in $\frac{1}{N}$. The auxiliary spinor gauge field acquires a nontrivial (nonlocal) dynamics with a generation of Maxwell and Chern-Simons noncommutative terms in the effective action. Up to the 1/N order all divergences are only logarithimic so that the model is free from nonintegrable infrared singularities.Comment: Minor corrections in the text and modifications in the list of reference

On the Renormalizability of Theories with Gauge Anomalies

We consider the detailed renormalization of two (1+1)-dimensional gauge theories which are quantized without preserving gauge invariance: the chiral and the "anomalous" Schwinger models. By regularizing the non-perturbative divergences that appear in fermionic Green's functions of both models, we show that the "tree level" photon propagator is ill-defined, thus forcing one to use the complete photon propagator in the loop expansion of these functions. We perform the renormalization of these divergences in both models to one loop level, defining it in a consistent and semi-perturbative sense that we propose in this paper.Comment: Final version, new title and abstract, introduction and conclusion rewritten, detailed semiperturbative discussion included, references added; to appear in International Journal of Modern Physics