Alejandro Cabo

Modified initial state for perturbative QCD

A particular initial state for the construction of the perturbative expansion of QCD is investigated. It is formed as a coherent superposition of zero momentum gluon pairs and shows Lorentz as well as global SU(3) symmetries. It follows that the gluon and ghost propagators determined by it, coincides with the ones used in an alternative of the usual perturbation theory proposed in a previous work. Therefore, the ability of such a procedure of producing a finite gluon condensation parameter already in the first orders of perturbation theory is naturally explained. It also follows that this state satisfies the physicality condition of the BRST procedure in its Kugo and Ojima formulation. The BRST quantization is done for the value alpha=1 of the gauge parameter where the procedure is greatly simplified. Therefore, after assuming that the adiabatic connection of the interaction does not take out the state from the interacting physical space, the predictions of the perturbation expansion, at the value alpha=1, for the physical quantities should have meaning. The validity of this conclusion solves the gauge dependence indeterminacy remained in the proposed perturbation expansion.

Gauge-invariance properties and singularity cancellations in a modified PQCD

The gauge-invariance properties and singularity elimination of the modified perturbation theory for QCD introduced in previous works are investigated. The construction of the modified free propagators is generalized to include the dependence on the gauge parameter α. Further, a functional proof of the independence of the theory under the changes of the quantum and classical gauges is given. The singularities appearing in the perturbative expansion are eliminated by properly combining dimensional regularization with the Nakanishi infrared regularization for the invariant functions in the operator quantization of the α-dependent gauge theory. First-order evaluations of various quantities are presented, illustrating the gauge-invariance properties.

The role of the Chern-Simons action for the description of the quantum Hall effect

Abstract The role of the Chern-Simons action in the description of the quantum Hall effect is stressed. The 2D electromagnetic picture of Widom and Srivastava is shown to be valid in a superlattice of 2D electron gases. A Meissner-like effect appears in such systems. In them, the difference between the external and the integer filling factor fields is exponentially screened by the surface (edge) currents. Also, effective Maxwell equations for one sheet or a superlattice are obtained.

Field configurations for small deviations of the integral filling factors in IQHE

Abstract A numerical solution of the effective Maxwell equations of the IQHE is presented. It corresponds to inhomogeneous electromagnetic field distributions appearing after a small constant magnetic field is added to a 2D-electron gas sheet when the density exactly fills an integral number of Landau levels. It follows that the Chern-Simons terms of the Maxwell equation transform the applied magnetic field into an equivalent homogeneous charge density. The numerical value of this density is exactly the one which is needed to furnish complete filling at the new value of the total magnetic field. The system then reacts tending to screen the effective charge density by removing charge from the sample edges. It is interesting that for the selected parameter values here, reflecting the current experimental situations, the system response is able to approximately establish an integral filling factor in the central portion of the sheet. Then, at least a small plateau is predicted to occur in pure samples at zero temperature. It also follows that the current distribution is unsymmetric under the inversion, as opposed to the configuration associated to a flow of a net Hall current at integral filling factors.

Exact diagonalization of the interacting propagator for the 2D electron gas in a magnetic field

The spatial dependence of the exact one electron propagator for an interacting 2D electron gas in a magnetic field is shown to be the same as for a non-interacting gas. This happens whenever the translational symmetry is unbroken in the ground state. The result may be extended to a more general class of systems. The translational symmetry also implies that the density of states has the same kind of discrete character as in the non-interacting case. This is shown explicitly in the Hartree-Fock approximation by solving the Dyson equation.

Zero momentum gluons and perturbative QCD

A modified initial state for the construction of the perturbative expansion of QCD is investigated. It is formed as a coherent superposition of zero momentum gluon pairs and shows Lorentz as well as global SU(3) symmetries. It follows that the gluon and ghost propagators determined by it, coincides with the ones used in an alternative of the usual perturbation theory proposed in a previous work. Therefore, the ability of such a procedure of producing a finite gluon condensation parameter already in the first orders of perturbation theory is naturally explained. It also follows that this state satisfies the physicality condition of the BRST procedure in its Kugo and Ojima formulation. Therefore, after assuming that the adiabatic connection of the interaction does not take out the state from the interacting physical space, the predictions of the perturbation expansion, for the physical quantities should have meaning.

Stability conditions and the single mode approximation in FQHE

Abstract A thermodynamic stability criterion for the spontaneous breaking of translation invariance in many particle systems is derived. It simply requires the positive character of the wavevector dependent dielectric function, generalishing the same condition for macroscopic dielectric constants. Its application to the single mode approximation (SMA) for the description of collective modes of the v = 1 m Laughlin states is considered. The results indicate that the stability condition is violated by the SMA for all the relevant states m = 3, 5, 7, 9 in a wavevector neighborhood of the magneto-roton minima. These conclusions are in qualitative agreement with similar results obtained from the solution of the Bethe-Salpeter equation at v = 1 3 for both composite fermions and phenomenologically described electrons in the Laughlin state.