585 research outputs found
Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations
Commutative sets of Jucys-Murphyelements for affine braid groups of
types were defined. Construction of
-matrix representations of the affine braid group of type and its
distinguish commutative subgroup generated by the -type Jucys--Murphy
elements are given. We describe a general method to produce flat connections
for the two-boundary quantum Knizhnik-Zamolodchikov equations as necessary
conditions for Sklyanin's type transfer matrix associated with the two-boundary
multicomponent Zamolodchikov algebra to be invariant under the action of the
-type Jucys--Murphy elements. We specify our general construction to
the case of the Birman--Murakami--Wenzl algebras. As an application we suggest
a baxterization of the Dunkl--Cherednik elements in the double affine
Hecke algebra of type
Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation
We report on the experimental study of an exceptional point (EP) in a
dissipative microwave billiard with induced time-reversal invariance (T)
violation. The associated two-state Hamiltonian is non-Hermitian and
non-symmetric. It is determined experimentally on a narrow grid in a parameter
plane around the EP. At the EP the size of T violation is given by the relative
phase of the eigenvector components. The eigenvectors are adiabatically
transported around the EP, whereupon they gather geometric phases and in
addition geometric amplitudes different from unity
A Quasi-Hopf algebra interpretation of quantum 3-j and 6-j symbols and difference equations
We consider the universal solution of the Gervais-Neveu-Felder equation in
the case. We show that it has a quasi-Hopf algebra
interpretation. We also recall its relation to quantum 3-j and 6-j symbols.
Finally, we use this solution to build a q-deformation of the trigonometric
Lam\'e equation.Comment: 9 pages, 4 figure
The irreducible unitary representations of the extended Poincare group in (1+1) dimensions
We prove that the extended Poincare group in (1+1) dimensions is
non-nilpotent solvable exponential, and therefore that it belongs to type I. We
determine its first and second cohomology groups in order to work out a
classification of the two-dimensional relativistic elementary systems.
Moreover, all irreducible unitary representations of the extended Poincare
group are constructed by the orbit method. The most physically interesting
class of irreducible representations corresponds to the anomaly-free
relativistic particle in (1+1) dimensions, which cannot be fully quantized.
However, we show that the corresponding coadjoint orbit of the extended
Poincare group determines a covariant maximal polynomial quantization by
unbounded operators, which is enough to ensure that the associated quantum
dynamical problem can be consistently solved, thus providing a physical
interpretation for this particular class of representations.Comment: 12 pages, Revtex 4, letter paper; Revised version of paper published
in J. Math. Phys. 45, 1156 (2004
Changes in Arctic Ocean Climate Evinced through Analysis of IPY 2007–2008 Oceanographic Observations
Full-depth hydrographical surveys conducted in 2007–2009 during the International Polar Year (IPY) collaboration provide an accurate snapshot of the Arctic Ocean (AO) hydrography at a time when the Arctic Ocean Oscillation (AOO) index was highest in recent record. We construct pan-Arctic temperature and salinity (T/S) reference states from these data using variational optimal interpolation and discuss some key differences between the 2007–2009 state and a similarly constructed climatology from historical 1950–1994 Russian archives. These data provide a recent, known reference state for both qualitative and quantitative future AO climate change studies. Furthermore, we present an analysis of sea-surface height (SSH) and upper-layer circulation constructed from the IPY data via 4DVar data assimilation and use them to examine circulation and freshwater source changes visible during IPY
Scaling functions from q-deformed Virasoro characters
We propose a renormalization group scaling function which is constructed from
q-deformed fermionic versions of Virasoro characters. By comparison with
alternative methods, which take their starting point in the massive theories,
we demonstrate that these new functions contain qualitatively the same
information. We show that these functions allow for RG-flows not only amongst
members of a particular series of conformal field theories, but also between
different series such as N=0,1,2 supersymmetric conformal field theories. We
provide a detailed analysis of how Weyl characters may be utilized in order to
solve various recurrence relations emerging at the fixed points of these flows.
The q-deformed Virasoro characters allow furthermore for the construction of
particle spectra, which involve unstable pseudo-particles.Comment: 31 pages of Latex, 5 figure
Quantum toboggans: models exhibiting a multisheeted PT symmetry
A generalization of the concept of PT-symmetric Hamiltonians H=p^2+V(x) is
described. It uses analytic potentials V(x) (with singularities) and a
generalized concept of PT-symmetric asymptotic boundary conditions. Nontrivial
toboggans are defined as integrated along topologically nontrivial paths of
coordinates running over several Riemann sheets of wave functions.Comment: 16 pp, 5 figs. Written version of the talk given during 5th
International Symposium on Quantum Theory and Symmetries, University of
Valladolid, Spain, July 22 - 28 2007, webpage http://tristan.fam.uva.es/~qts
Quantization of Field Theories Generalizing Gravity-Yang-Mills Systems on the Cylinder
Pure gravity and gauge theories in two dimensions are shown to be special
cases of a much more general class of field theories each of which is
characterized by a Poisson structure on a finite dimensional target space. A
general scheme for the quantization of these theories is formulated. Explicit
examples are studied in some detail. In particular gravity and gauge theories
with equivalent actions are compared. Big gauge transformations as well as the
condition of metric nondegeneracy in gravity turn out to cause significant
differences in the structure of the corresponding reduced phase spaces and the
quantum spectra of Dirac observables. For gravity coupled to SU(2) Yang
Mills the question of quantum dynamics (`problem of time') is addressed. [This
article is a contribution to the proceedings (to appear in LNP) of the 3rd
Baltic RIM Student Seminar (1993). Importance is attached to concrete examples.
A more abstract presentation of the ideas underlying this article (including
new developments) is found in hep-th/9405110.]Comment: 26, pages, TUW-94-
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