Comment on "Attractive Forces between Electrons in 2 + 1 Dimensional QED"

It is shown that a model recently proposed for numerical calculations of bound states in QED$_3$ is in fact an improper truncation of the Aharonov-Bohm potential.Comment: 4 page

Nonperturbative solution of the Nonconfining Schwinger Model with a generalized regularization

Nonconfining Schwinger Model [AR] is studied with a one parameter class of kinetic energy like regularization. It may be thought of as a generalization over the regularization considered in [AR]. Phasespace structure has been determined in this new situation. The mass of the gauge boson acquires a generalized expression with the bare coupling constant and the parameters involved in the regularization. Deconfinement scenario has become transparent at the quark-antiquark potential level.Comment: 13 pages latex fil

Canonical Quantization of the Self-Dual Model coupled to Fermions

This paper is dedicated to formulate the interaction picture dynamics of the self-dual field minimally coupled to fermions. To make this possible, we start by quantizing the free self-dual model by means of the Dirac bracket quantization procedure. We obtain, as result, that the free self-dual model is a relativistically invariant quantum field theory whose excitations are identical to the physical (gauge invariant) excitations of the free Maxwell-Chern-Simons theory. The model describing the interaction of the self-dual field minimally coupled to fermions is also quantized through the Dirac bracket quantization procedure. One of the self-dual field components is found not to commute, at equal times, with the fermionic fields. Hence, the formulation of the interaction picture dynamics is only possible after the elimination of the just mentioned component. This procedure brings, in turns, two new interaction terms, which are local in space and time while non-renormalizable by power counting. Relativistic invariance is tested in connection with the elastic fermion-fermion scattering amplitude. We prove that all the non-covariant pieces in the interaction Hamiltonian are equivalent to the covariant minimal interaction of the self-dual field with the fermions. The high energy behavior of the self-dual field propagator corroborates that the coupled theory is non-renormalizable. Certainly, the self-dual field minimally coupled to fermions bears no resemblance with the renormalizable model defined by the Maxwell-Chern-Simons field minimally coupled to fermions.Comment: 16 pages, no special macros, no corrections in the pape

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

The noncommutative degenerate electron gas

The quantum dynamics of nonrelativistic single particle systems involving noncommutative coordinates, usually referred to as noncommutative quantum mechanics, has lately been the object of several investigations. In this note we pursue these studies for the case of multi-particle systems. We use as a prototype the degenerate electron gas whose dynamics is well known in the commutative limit. Our central aim here is to understand qualitatively, rather than quantitatively, the main modifications induced by the presence of noncommutative coordinates. We shall first see that the noncommutativity modifies the exchange correlation energy while preserving the electric neutrality of the model. By employing time-independent perturbation theory together with the Seiberg-Witten map we show, afterwards, that the ionization potential is modified by the noncommutativity. It also turns out that the noncommutative parameter acts as a reference temperature. Hence, the noncommutativity lifts the degeneracy of the zero temperature electron gas.Comment: 11 pages, to appear in J. Phys. A: Math. Ge

Attractive Forces Between Electrons in QED3_{3}

Vacuum polarization effects are non-perturbatively incorporated into the photon propagator to eliminate the severe infrared problems characteristic of QED$_3$. The theory is thus rephrased in terms of a massive vector boson whose mass is $e^2/(8\pi)$. Subsequently, it is shown that electron-electron bound states are possible in QED$_3$.Comment: revtex, 10 pages and four figures, IFUSP/P-98

Exact Renormalization of Massless QED2

We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.Comment: 14 pages, no figures, introduction and conclusions modifie