Spin-Charge Separation and the Pauli Electron

The separation between the spin and the charge converts the quantum mechanical Pauli Hamiltonian into the Hamiltonian of the non-Abelian Georgi-Glashow model, notorious for its magnetic monopoles and confinement. The independent spin and charge fluctuations both lead to the Faddeev model, suggesting the existence of a deep duality structure and indicating that the fundamental carriers of spin and charge are knotted solitons.Comment: 7 pages; v2: new results added, references update

On the Class of Possible Nonlocal Anyon-Like Operators and Quantum Groups

We find a class of nonlocal operators constructed by attaching a disorder operator to fermionic degrees of freedom, which can be used to generate q-deformed algebras following the Schwinger approach. This class includes the recently proposed anyonic operators defined on a lattice.Comment: 10 pages (plain latex), HU-SEFT R 1993-9, to be published in Journal of Physics A: Math. and General, Letters to the Edito

Chiral solitons from dimensional reduction of Chern-Simons gauged non-linear Schr\"odinger model of FQHE: classical and quantum aspects

The soliton structure of a gauge theory recently proposed to describe chiral excitations in the Fractional Quantum Hall Effect is investigated. A new type of non-linear derivative Schr\"odinger equation emerges as an effective description of the system that supports novel chiral solitons. We discuss the classical properties of solutions with vanishing and non-vanishing boundary conditions (dark solitons) and we explain their relation to integrable systems. The quantum analysis is also addressed in the framework of a semiclassical approximation improved by Renormalization Group arguments.Comment: 39 page, RevTeX, 6 figure

Generalized transformation optics from triple spacetime metamaterials

In this paper various extensions of the design strategy of transformation media are proposed. We show that it is possible to assign different transformed spaces to the field strength tensor (electric field and magnetic induction) and to the excitation tensor (displacement field and magnetic field), resp. In this way, several limitations of standard transformation media can be overcome. In particular it is possible to provide a geometric interpretation of non-reciprocal as well as indefinite materials. We show that these transformations can be complemented by a continuous version of electric-magnetic duality and comment on the relation to the complementary approach of field-transforming metamaterials.Comment: 11 pages, 3 figures, v2: typos, new figures, REVTeX, v3: typos, new example added, final versio

Evidence for Non-perturbative String Symmetries

String theory appears to admit a group of discrete field transformations -- called $S$ dualities -- as exact non-perturbative quantum symmetries. Mathematically, they are rather analogous to the better-known $T$ duality symmetries, which hold perturbatively. In this talk the evidence for $S$ duality is reviewed and some speculations are presented.Comment: Error corrected and reference added; 10 pages, latex, no figures, conference Repor

Statistics of Q-Oscillators, Quons and Relation to Fractional Satistics

The statistics of $q$-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic $q$-oscillators are found for their corresponding Fock space representations in the case when the hamiltonian is identified with the number operator. In this case and for nonrelativistic particles, the single-particle temperature Green function is defined with $q$-deformed periodicity conditions. The equations of state for nonrelativistic and ultrarelativistic bosonic $q$-gases in an arbitrary space dimension are found near Bose statistics, as well as the one for an anyonic gas near Bose and Fermi statistics. The first corrections to the second virial coefficients are also evaluated. The phenomenon of Bose-Einstein condensation in the $q$-deformed gases is also discussed.Comment: 21 pages, Latex, HU-TFT-93-2

Symmetry transform in the Faddeev-Jackiw quantization of dual models

We study the presence of symmetry transformations in the Faddeev-Jackiw approach for constrained systems. Our analysis is based in the case of a particle submitted to a particular potential which depends on an arbitrary function. The method is implemented in a natural way and symmetry generators are identified. These symmetries permit us to obtain the absent elements of the sympletic matrix which complement the set of Dirac brackets of such a theory. The study developed here is applied in two different dual models. First, we discuss the case of a two-dimensional oscillator interacting with an electromagnetic potential described by a Chern-Simons term and second the Schwarz-Sen gauge theory, in order to obtain the complete set of non-null Dirac brackets and the correspondent Maxwell electromagnetic theory limit.Comment: 22 pages, RevTex file, no figur

Scaling of Aharonov-Bohm couplings and the dynamical vacuum in gauge theories

Recent results on the vacuum polarization induced by a thin string of magnetic flux lead us to suggest an analogue of the Copenhagen `flux spaghetti' QCD vacuum as a possible mechanism for avoiding the divergence of perturbative QED, thus permitting consistent completion of the full, nonperturbative theory. The mechanism appears to operate for spinor, but not scalar, QED.Comment: 11 pages, ITP-SB-92-40, (major conceptual evolution from original

Reducing SS- duality to TT- duality

The infrared limit of $D=4,~~N=4$ Yang-Mills theory with compact gauge group $G$ compactified on a two-torus is governed by an effective superconformal field theory. We conjecture that this is a certain orbifold involving the maximal torus of $G$. Yang-Mills $S$-duality makes predictions for all correlators of this effective conformal field theory. These predictions are shown to be implied by the standard $T$-duality of the conformal field theory. Consequently, Montonen-Olive duality between electric and magnetic states reduces to the standard two-dimensional duality between momentum and winding states.Comment: 13 pages, harvmac, no figures. (Some Comments added. Some references added.