Edge waves in the quantum hall effect

Edge waves in the quantum hall effect

ANNALS OF PHYSICS 206, 255-256 Abstracts (1991) of Papers to Appear in Future Issues Relativistic SU(6) Wave Functions as the Basis of Modern A...

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ANNALS OF PHYSICS 206, 255-256

Abstracts

(1991)

of Papers

to Appear

in Future

Issues

Relativistic SU(6) Wave Functions as the Basis of Modern Approaches to Hadronic Wave Functions. F. HUSSAIN, J. G. K~RNER, AND G. THOMPSON. Institut fur Physik, Johannes-Gutenberg-Universitat, Staudinger Weg 7, Postfach 3980, D-6500 Mainz, Germany. The connections between various models of hadrons and the relativistic SU(6) wave functions are established. In formal terms and by concrete example it is shown how the Bargman-Wigner fields of freely moving quarks and antiquarks of equal velocity form the basis of the above approaches. This places modern attempts in their historical setting and allows for a more unified analysis of the various schemes.

SL(N)

Kac-Moody Algebras Universitlt Kaiserslautern,

and Wess-Zumin+Witten Kaiserslautern, Germany.

Wess-Zumino-Witten models are represented is used to reduce arbitrary three-point functions

Fermi

Gas Descriptions of Nuclear Institute of Theoretical Physics,

by Wakimoto to generalized

Models.

W.

R~~HL.

Fachbereich

Physik,

modules. Representation theory Dotsenko-Fateev integrals.

of X(N)

Level Densities. C. A. ENGELBRECHT AND J. R. ENGELBRECHT. University of Stellenbosch, 7600 Stellenbosch, South Africa.

In this paper the derivation of nuclear level densities from a Fermi gas treatment of the nucleons is surveyed. In fact, there are three classes of Fermi gas models: the infinite, in which an unlimited number of fermions are available for excitation, the finite, in which this number is finite but the single-particle spectrum is unbounded, and the truncated Fermi gas (TFG), where this spectrum consists of a finite number of levels. Exact calculations within the TFG are possible by means of combinatorial methods, while the finite model may be analysed by assuming that the assumptions of statistical mechanics apply to the numbers of nucleons in a nucleus and then using a saddle point approximation. The standard Bethe formulae actually correspond to the infinite model and apply to the other models only in the lowenergy limit. Furthermore, at very low energies they do not approximate any of the models with high accuracy and should there be corrected, as indicated in the text. For high-energy or high-temperature applications, it is essential to take into account the effects of truncation. The TFG is constructed here in a way which accommodates the two main features in which the results for real interacting nucleons should differ from the Fermi gas picture. In order to make the TFG results accessible for practical applications without having to perform the cumbersome combinatorial calculations for each case of interest, simple approximations are presented for the nuclear level densities, as well as the closely related canonical partition functions, as obtained by means of calculations using the truncated Fermi gas model.

Edge Waves in the Quantum Department of Physics, I show that two-dimensional

Hall Effect. MICHAEL STONE. University of Illinois 1110 West Green Street, Urbana, Illinois 61801.

at Urbana

Champaign,

the bosonized form of the low energy edge excitations at the surface of a droplet of quantum Hall liquid can be understood in terms of coherent “ripplon” deformations

255 0003-49

1619 1 $7.50

Copyright 10 1991 by Academic Press. Inc. All rights of reproduction in any lorm reserved.

256

ABSTRACTS

OF PAPERS

TO APPEAR

IN

FUTURE

ISSUES

in the shape of the droplet. When interacting with an electromagnetic held the resulting chiral boson theory has anomalies that are cancelled, via the Callan-Harvey mechanism, by contributions from the bulk. I also consider non-Abelian generalization of the bosonization that may be useful for chiral spin states.

The RPA-SPA Approximation sez. di Milano, I-20133 Milano, and Istituto AND R. A. BROGLIA. Fisica Nucleare sez. di Copenhagen, Dk-2100

to Level Densities. G. PUDDU. Istituto Nazionale di Fisica Nucleare Milano, Italy; P. F. BORTIGNON. Istituto di Ingegneria, Politecnico di Nazionale di Fisica Nucleare sez. di Milano, I-20133 Milano, Italy; Dipartimento di Fisica, Universita di Milano, and Istituto Nazionale di Milano, I-20133 Milano, Italy, and The Niels Bohr Institute, University of Copenhagen, Denmark.

Functional integral techniques are applied to the problem of level densities for interacting Fermi systems. Thermal and small-amplitude quanta1 fluctuations are retained in the partition function. Validity and limitations of the approximation are explored on solvable models for which the mean-field approximation displays phase transitions. The exact results are reproduced to a high level of accuracy.

Bosonization

of Parafermions and Related Conformal Models: W,-Algebras. FRANCISCO J. NARGANESService de Physique Theorique, Universite Libre de Bruxelles, CP 225, Boulevard du Triomphe, B-1050 Brussels, Belgium. QUIJANO.

Following a coset-inspired construction, we obtain a representation of the symmetry currents of a large number of extended conformal models in terms of free bosonic fields. In particular we bosonize the [Z,], [D3], and [Da] parafermionic current algebras and some conformal models closely related to them. The bosonized expression of the Z, parafermionic currents gives rise to a set of local currents that can be identified, up to null-currents, with a W,-algebra; the hidden connection between the [iZN] parafermions and the [ W,] p = NC ’ non-linearly extended conformal models is thus exhibited in a manifest way. A special feature of this W,-algebra is its realization in terms of only two bosonic fields.

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