388 research outputs found
Chern-Simons Theory with Sources and Dynamical Quantum Groups I: Canonical Analysis and Algebraic Structures
We study the quantization of Chern-Simons theory with group coupled to
dynamical sources. We first study the dynamics of Chern-Simons sources in the
Hamiltonian framework. The gauge group of this system is reduced to the Cartan
subgroup of We show that the Dirac bracket between the basic dynamical
variables can be expressed in term of dynamical matrix of rational type.
We then couple minimally these sources to Chern-Simons theory with the use of
a regularisation at the location of the sources. In this case, the gauge
symmetries of this theory split in two classes, the bulk gauge transformation
associated to the group and world lines gauge transformations associated to
the Cartan subgroup of . We give a complete hamiltonian analysis of this
system and analyze in detail the Poisson algebras of functions invariant under
the action of bulk gauge transformations. This algebra is larger than the
algebra of Dirac observables because it contains in particular functions which
are not invariant under reparametrization of the world line of the sources. We
show that the elements of this Poisson algebra have Poisson brackets expressed
in term of dynamical matrix of trigonometric type. This algebra is a
dynamical generalization of Fock-Rosly structure. We analyze the quantization
of these structures and describe different star structures on these algebras,
with a special care to the case where and
having in mind to apply these results to the
study of the quantization of massive spinning point particles coupled to
gravity with a cosmological constant in 2+1 dimensions.Comment: 32 pages and 1 eps figur
Harmonic Analysis on the quantum Lorentz group
This work begins with a review of complexification and realification of Hopf
algebras. We emphasize the notion of multiplier Hopf algebras for the
description of different classes of functions (compact supported, bounded,
unbounded) on complex quantum groups and the construction of the associated
left and right Haar measure. Using a continuation of symbols of
with complex spins, we give a new description of the unitary representations of
SL_q (2,\CC)_{\RR} and find explicit expressions for the characters of SL_q
(2,\CC)_{\RR}. The major theorem of this article is the Plancherel theorem for
the Quantum Lorentz Group.Comment: 60 pages, tared gzipped Postscript file, major revision of the
previous version, the Plancherel theorem is established in the more general
sense and we delay the study of Fusion theory to the next part of this pape
Quantum Dynamical coBoundary Equation for finite dimensional simple Lie algebras
For a finite dimensional simple Lie algebra g, the standard universal
solution R(x) in of the Quantum Dynamical Yang--Baxter
Equation can be built from the standard R--matrix and from the solution F(x) in
of the Quantum Dynamical coCycle Equation as
It has been conjectured that, in the case
where g=sl(n+1) n greater than 1 only, there could exist an element M(x) in
such that in which is
the universal cocycle associated to the Cremmer--Gervais's solution. The aim of
this article is to prove this conjecture and to study the properties of the
solutions of the Quantum Dynamical coBoundary Equation. In particular, by
introducing new basic algebraic objects which are the building blocks of the
Gauss decomposition of M(x), we construct M(x) in as an explicit
infinite product which converges in every finite dimensional representation. We
emphasize the relations between these basic objects and some Non Standard Loop
algebras and exhibit relations with the dynamical quantum Weyl group.Comment: 46 page
Universal Solutions of Quantum Dynamical Yang-Baxter Equations
We construct a universal trigonometric solution of the Gervais-Neveu-Felder
equation in the case of finite dimensional simple Lie algebras and finite
dimensional contragredient simple Lie superalgebras.Comment: 12 pages, LaTeX2e with packages vmargin, wasysym, amsmath, amssym
6J Symbols Duality Relations
It is known that the Fourier transformation of the square of (6j) symbols has
a simple expression in the case of su(2) and U_q(su(2)) when q is a root of
unit. The aim of the present work is to unravel the algebraic structure behind
these identities. We show that the double crossproduct construction H_1\bowtie
H_2 of two Hopf algebras and the bicrossproduct construction H_2^{*}\lrbicross
H_1 are the Hopf algebras structures behind these identities by analysing
different examples. We study the case where D= H_1\bowtie H_2 is equal to the
group algebra of ISU(2), SL(2,C) and where D is a quantum double of a finite
group, of SU(2) and of U_q(su(2)) when q is real.Comment: 28 pages, 2 figure
Competition between magnetic field dependent band structure and coherent backscattering in multiwall carbon nanotubes
Magnetotransport measurements in large diameter multiwall carbon nanotubes
(20-40 nm) demonstrate the competition of a magnetic-field dependent
bandstructure and Altshuler-Aronov-Spivak oscillations. By means of an
efficient capacitive coupling to a backgate electrode, the magnetoconductance
oscillations are explored as a function of Fermi level shift. Changing the
magnetic field orientation with respect to the tube axis and by ensemble
averaging, allows to identify the contributions of different Aharonov-Bohm
phases. The results are in qualitative agreement with numerical calculations of
the band structure and the conductance.Comment: 4 figures, 5 page
Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory
We define and study the properties of observables associated to any link in
(where is a compact surface) using the
combinatorial quantization of hamiltonian Chern-Simons theory. These
observables are traces of holonomies in a non commutative Yang-Mills theory
where the gauge symmetry is ensured by a quantum group. We show that these
observables are link invariants taking values in a non commutative algebra, the
so called Moduli Algebra. When these link invariants are pure
numbers and are equal to Reshetikhin-Turaev link invariants.Comment: 39, latex, 7 figure
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