Hopf algebraic structure of the parabosonic and parafermionic algebras and paraparticle generalization of the Jordan Schwinger map

The aim of this paper is to show that there is a Hopf structure of the parabosonic and parafermionic algebras and this Hopf structure can generate the well known Hopf algebraic structure of the Lie algebras, through a realization of Lie algebras using the parabosonic (and parafermionic) extension of the Jordan Schwinger map. The differences between the Hopf algebraic and the graded Hopf superalgebraic structure on the parabosonic algebra are discussed.Comment: 11 pages, LaTex2e fil

Algebraic structure of the Green's ansatz and its q-deformed analogue

The algebraic structure of the Green's ansatz is analyzed in such a way that its generalization to the case of q-deformed para-Bose and para-Fermi operators is becoming evident. To this end the underlying Lie (super)algebraic properties of the parastatistics are essentially used.Comment: plain TeX, Preprint INRNE-TH-94/4, 13

Real Forms of the Oscillator Quantum Algebra and its Representations

We consider the conditions under which the $q$-oscillator algebra becomes a Hopf $*$-algebra. In particular, we show that there are at least two real forms associated with the algebra. Furthermore, through the representations, it is shown that they are related to ${\text {su}}_{q^{1/2}}(2)$ with different conjugations.Comment: 10 pages, Ams-Tex, To be published in Letters in Mathematical physic

Unitarizable Representations of the Deformed Para-Bose Superalgebra Uq[osp(1/2)] at Roots of 1

The unitarizable irreps of the deformed para-Bose superalgebra $pB_q$, which is isomorphic to $U_q[osp(1/2)]$, are classified at $q$ being root of 1. New finite-dimensional irreps of $U_q[osp(1/2)]$ are found. Explicit expressions for the matrix elements are written down.Comment: 19 pages, PlainTe

Macroscopic properties of A-statistics

A-statistics is defined in the context of the Lie algebra sl(n+1). Some thermal properties of A-statistics are investigated under the assumption that the particles interact only via statistical interaction imposed by the Pauli principle of A-statistics. Apart from the general case, three particular examples are studied in more detail: (a) the particles have one and the same energy and chemical potential; (b) equidistant energy spectrum; (c) two species of particles with one and the same energy and chemical potential within each class. The grand partition functions and the average number of particles are among the thermodynamical quantities written down explicitly.Comment: 27 pages, 4 figures; to be published in J. Phys.

Hyperfine Fields in an Ag/Fe Multilayer Film Investigated with 8Li beta-Detected Nuclear Magnetic Resonance

Low energy $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) was used to investigate the spatial dependence of the hyperfine magnetic fields induced by Fe in the nonmagnetic Ag of an Au(40 \AA)/Ag(200 \AA)/Fe(140 \AA) (001) magnetic multilayer (MML) grown on GaAs. The resonance lineshape in the Ag layer shows dramatic broadening compared to intrinsic Ag. This broadening is attributed to large induced magnetic fields in this layer by the magnetic Fe layer. We find that the induced hyperfine field in the Ag follows a power law decay away from the Ag/Fe interface with power $-1.93(8)$, and a field extrapolated to $0.23(5)$ T at the interface.Comment: 5 pages, 4 figure. To be published in Phys. Rev.

Lorentz transformation and vector field flows

The parameter changes resulting from a combination of Lorentz transformation are shown to form vector field flows. The exact, finite Thomas rotation angle is determined and interpreted intuitively. Using phase portraits, the parameters evolution can be clearly visualized. In addition to identifying the fixed points, we obtain an analytic invariant, which correlates the evolution of parameters.Comment: 11 pages, 3 figures. Section IV revised and title change

β\beta-NMR of Isolated 8^{8}Li+^{+} Implanted into a Thin Copper Film

Depth-controlled $\beta$-NMR was used to study highly spin-polarized $^8$Li in a Cu film of thickness 100 nm deposited onto a MgO substrate. The positive Knight Shifts and spin relaxation data show that $^8$Li occupies two sites at low temperatures, assigned to be the substitutional ($S$) and octahedral ($O$) interstitial sites. Between 50 to 100 K, there is a site change from $O$ to $S$. The temperature dependence of the Knight shifts and spin-lattice relaxation rates at high temperatures, i.e. when all the Li are in the $S$ site, is consistent with the Korringa Law for a simple metal.Comment: Accepted for publication in Phys. Rev.

Fock representations of the superalgebra sl(n+1|m), its quantum analogue U_q[sl(n+1|m)] and related quantum statistics

Fock space representations of the Lie superalgebra $sl(n+1|m)$ and of its quantum analogue $U_q[sl(n+1|m)]$ are written down. The results are based on a description of these superalgebras via creation and annihilation operators. The properties of the underlying statistics are shortly discussed.Comment: 12 pages, PlainTex; to appear in J. Phys. A: Math. Ge

New Solutions of the Yang-Baxter Equation Based on Root of 1 Representations of the Para-Bose Superalgebra Uq_q[osp(1/2)]

New solutions of the quantum Yang-Baxter equation, depending in general on three arbitrary parameters, are written down. They are based on the root of unity representations of the quantum orthosymplectic superalgebra \\U, which were found recently. Representations of the braid group $B_N$ are defined within any $N^{th}$ tensorial power of root of 1 \\U modules.Comment: 11 pages, PlainTe