1,500 research outputs found
Two-dimensional quantum liquids from interacting non-Abelian anyons
A set of localized, non-Abelian anyons - such as vortices in a p_x + i p_y
superconductor or quasiholes in certain quantum Hall states - gives rise to a
macroscopic degeneracy. Such a degeneracy is split in the presence of
interactions between the anyons. Here we show that in two spatial dimensions
this splitting selects a unique collective state as ground state of the
interacting many-body system. This collective state can be a novel gapped
quantum liquid nucleated inside the original parent liquid (of which the anyons
are excitations). This physics is of relevance for any quantum Hall plateau
realizing a non-Abelian quantum Hall state when moving off the center of the
plateau.Comment: 5 pages, 6 figure
The Gervais-Neveu-Felder equation for the Jordanian quasi-Hopf U_{h;y}(sl(2)) algebra
Using a contraction procedure, we construct a twist operator that satisfies a
shifted cocycle condition, and leads to the Jordanian quasi-Hopf U_{h;y}(sl(2))
algebra. The corresponding universal matrix obeys a
Gervais-Neveu-Felder equation associated with the U_{h;y}(sl(2)) algebra. For a
class of representations, the dynamical Yang-Baxter equation may be expressed
as a compatibility condition for the algebra of the Lax operators.Comment: Latex, 9 pages, no figure
Cotensor Coalgebras in Monoidal Categories
We introduce the concept of cotensor coalgebra for a given bicomodule over a
coalgebra in an abelian monoidal category. Under some further conditions we
show that such a cotensor coalgebra exists and satisfies a meaningful universal
property. We prove that this coalgebra is formally smooth whenever the comodule
is relative injective and the coalgebra itself is formally smooth
Centre and Representations of U_q(sl(2|1)) at Roots of Unity
Quantum groups at roots of unity have the property that their centre is
enlarged. Polynomial equations relate the standard deformed Casimir operators
and the new central elements. These relations are important from a physical
point of view since they correspond to relations among quantum expectation
values of observables that have to be satisfied on all physical states. In this
paper, we establish these relations in the case of the quantum Lie superalgebra
U_q(sl(2|1)). In the course of the argument, we find and use a set of
representations such that any relation satisfied on all the representations of
the set is true in U_q(sl(2|1)). This set is a subset of the set of all the
finite dimensional irreducible representations of U_q(sl(2|1)), that we
classify and describe explicitly.Comment: Minor corrections, References added. LaTeX2e, 18 pages, also
available at http://lapphp0.in2p3.fr/preplapp/psth/ENSLAPP583.ps.gz . To
appear in J. Phys. A: Math. Ge
The Hopf modules category and the Hopf equation
We study the Hopf equation which is equivalent to the pentagonal equation,
from operator algebras. A FRT type theorem is given and new types of quantum
groups are constructed. The key role is played now by the classical Hopf
modules category. As an application, a five dimensional noncommutative
noncocommutative bialgebra is given.Comment: 30 pages, Letax2e, Comm. Algebra in pres
Global analysis by hidden symmetry
Hidden symmetry of a G'-space X is defined by an extension of the G'-action
on X to that of a group G containing G' as a subgroup. In this setting, we
study the relationship between the three objects:
(A) global analysis on X by using representations of G (hidden symmetry);
(B) global analysis on X by using representations of G';
(C) branching laws of representations of G when restricted to the subgroup
G'.
We explain a trick which transfers results for finite-dimensional
representations in the compact setting to those for infinite-dimensional
representations in the noncompact setting when is -spherical.
Applications to branching problems of unitary representations, and to spectral
analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th
birthda
Perturbative Symmetries on Noncommutative Spaces
Perturbative deformations of symmetry structures on noncommutative spaces are
studied in view of noncommutative quantum field theories. The rigidity of
enveloping algebras of semi-simple Lie algebras with respect to formal
deformations is reviewed in the context of star products. It is shown that
rigidity of symmetry algebras extends to rigidity of the action of the symmetry
on the space. This implies that the noncommutative spaces considered can be
realized as star products by particular ordering prescriptions which are
compatible with the symmetry. These symmetry preserving ordering prescriptions
are calculated for the quantum plane and four-dimensional quantum Euclidean
space. Using these ordering prescriptions greatly facilitates the construction
of invariant Lagrangians for quantum field theory on noncommutative spaces with
a deformed symmetry.Comment: 16 pages; LaTe
One-loop Effective Potential for a Fixed Charged Self-interacting Bosonic Model at Finite Temperature with its Related Multiplicative Anomaly
The one-loop partition function for a charged self-interacting Bose gas at
finite temperature in D-dimensional spacetime is evaluated within a path
integral approach making use of zeta-function regularization. For D even, a new
additional vacuum term ---overlooked in all previous treatments and coming from
the multiplicative anomaly related to functional determinants-- is found and
its dependence on the mass and chemical potential is obtained. The presence of
the new term is shown to be crucial for having the factorization invariance of
the regularized partition function. In the non interacting case, the
relativistic Bose-Einstein condensation is revisited. By means of a suitable
charge renormalization, for D=4 the symmetry breaking phase is shown to be
unaffected by the new term, which, however, gives actually rise to a non
vanishing new contribution in the unbroken phase.Comment: 25 pages, RevTex, a new Section and several explanations added
concering the non-commutative residue and the physical discussio
Quantum spin coverings and statistics
SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the
complex rotation group SO(3,C), in terms of the associated Hopf algebras of
(quantum) polynomial functions. We work out the irreducible corepresentations,
the decomposition of their tensor products and a coquasitriangular structure,
with the associated braiding (or statistics). As an example, the case l=3 is
discussed in detail.Comment: 15 page
Factorizable ribbon quantum groups in logarithmic conformal field theories
We review the properties of quantum groups occurring as Kazhdan--Lusztig dual
to logarithmic conformal field theory models. These quantum groups at even
roots of unity are not quasitriangular but are factorizable and have a ribbon
structure; the modular group representation on their center coincides with the
representation on generalized characters of the chiral algebra in logarithmic
conformal field models.Comment: 27pp., amsart++, xy. v2: references added, some other minor addition
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