The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems

Wen's chiral Tomonaga-Luttinger model for the edge of an m-layer quantum Hall system of total filling factor nu=m/(pm +- 1) with even p, is derived as a random-phase approximation of the Chern-Simons theory for these states. The theory allows for a description of edges both in and out of equilibrium, including their collective excitation spectrum and the tunneling exponent into the edge. While the tunneling exponent is insensitive to the details of a nu=m/(pm + 1) edge, it tends to decrease when a nu=m/(pm - 1) edge is taken out of equilibrium. The applicability of the theory to fractional quantum Hall states in a single layer is discussed.Comment: 15 page

Parafermions, parabosons and representations of so(\infty) and osp(1|\infty)

The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(\infty) and of the Lie superalgebra osp(1|\infty). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labelled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. We also present expressions for the character of the Fock space representations

The Paths of Unification In The GUST With The G x G Gauge Groups of E(8) x E(8)

In the framework of the four dimensional heterotic superstring with free fermions we discuss the rank eight and/or sixteen Grand Unified String Theories (GUST) which contain the SU(3)_H - gauge family symmetry. We explicitly investigate the paths of the unification in the GUST with gauge symmetry G x G = [SU(5) x U(1) x (SU(3) x U(1))_H]^2. We show that the GUSTs with the G x G gauge group allow to make the scale of unification to be consistent with the string scale M_SU = g_{string} * 5 * 10^17 GeV.Comment: 18 pages, 2 Postscript figures, uses epsf.st

Dynamics of Fluxon Lattice in Two Coupled Josephson Junctions

We study theoretically the dynamics of a fluxon Lattice (FL) in two coupled Josephson junctions. We show that when the velocity of the moving FL exceeds certain values $(V_{a,b})$, sharp resonances arise in the system which are related to the excitation of the optical and acoustic collective modes. In the interval $(V_a, V_b)$ a reconstruction of the FL occurs. We also establish that one can excite localized nonlinear distortions (dislocations) which may propagate through the FL and carry an arbitrary magnetic flux.Comment: 4 pages, 3 figures, corected typo

The Fermion Generations Problem in the Gust in the Free World-Sheet Fermion Formulation

In the framework of the four dimensional heterotic superstring with free fermions we present a revised version of the rank eight Grand Unified String Theories (GUST) which contain the $SU(3)_H$-gauge family symmetry. We also develop some methods for building of corresponding string models. We explicitly construct GUST with gauge symmetry $G = SU(5) \times U(1)\times (SU(3) \times U(1))_H$ and $G = SO(10)\times (SU(3) \times U(1))_H$ or $E(6)\times SU(3)_H$ $\subset E(8)$ and consider the full massless spectrum for our string models. We consider for the observable gauge symmetry the diagonal subgroup $G^{symm}$ of the rank 16 group $G \times G$ $\subset SO(16) \times SO(16)$ or $\subset E(8) \times E(8)$. We discuss the possible fermion matter and Higgs sectors in these theories. We study renormalizable and nonrenormolizable contributions to the superpotential. There has to exist "superweak" light chiral matter ($m_H^f < M_W$) in GUST under consideration. The understanding of quark and lepton mass spectra and family mixing leaves a possibility for the existence of an unusually low mass breaking scale of the $SU(3)_H$ family gauge symmetry (some TeV).Comment: 68 page