3,047 research outputs found
Operator Coproduct-Realization of Quantum Group Transformations in Two Dimensional Gravity, I.
A simple connection between the universal matrix of (for
spins \demi and ) and the required form of the co-product action of the
Hilbert space generators of the quantum group symmetry is put forward. This
gives an explicit operator realization of the co-product action on the
covariant operators. It allows us to derive the quantum group covariance of the
fusion and braiding matrices, although it is of a new type: the generators
depend upon worldsheet variables, and obey a new central extension of
realized by (what we call) fixed point commutation relations. This
is explained by showing that the link between the algebra of field
transformations and that of the co-product generators is much weaker than
previously thought. The central charges of our extended algebra,
which includes the Liouville zero-mode momentum in a nontrivial way are related
to Virasoro-descendants of unity. We also show how our approach can be used to
derive the Hopf algebra structure of the extended quantum-group symmetry
U_q(sl(2))\odot U_{\qhat}(sl(2)) related to the presence of both of the
screening charges of 2D gravity.Comment: 33 pages, latex, no figure
The Quantum Group Structure of 2D Gravity and Minimal Models II: The Genus-Zero Chiral Bootstrap
The F and B matrices associated with Virasoro null vectors are derived in
closed form by making use of the operator-approach suggested by the Liouville
theory, where the quantum-group symmetry is explicit. It is found that the
entries of the fusing and braiding matrices are not simply equal to
quantum-group symbols, but involve additional coupling constants whose
derivation is one aim of the present work. Our explicit formulae are new, to
our knowledge, in spite of the numerous studies of this problem. The
relationship between the quantum-group-invariant (of IRF type) and
quantum-group-covariant (of vertex type) chiral operator-algebras is fully
clarified, and connected with the transition to the shadow world for
quantum-group symbols. The corresponding 3-j-symbol dressing is shown to reduce
to the simpler transformation of Babelon and one of the author (J.-L. G.) in a
suitable infinite limit defined by analytic continuation. The above two types
of operators are found to coincide when applied to states with Liouville
momenta going to in a suitable way. The introduction of
quantum-group-covariant operators in the three dimensional picture gives a
generalisation of the quantum-group version of discrete three-dimensional
gravity that includes tetrahedra associated with 3-j symbols and universal
R-matrix elements. Altogether the present work gives the concrete realization
of Moore and Seiberg's scheme that describes the chiral operator-algebra of
two-dimensional gravity and minimal models.Comment: 56 pages, 22 figures. Technical problem only, due to the use of an
old version of uuencode that produces blank characters some times suppressed
by the mailer. Same content
Structural Implications of Persistent Disharmony in North American Beef and Pork Industries
Industrial Organization, Livestock Production/Industries,
Alien Registration- Gervais, Amanda C. (Fort Fairfield, Aroostook County)
https://digitalmaine.com/alien_docs/35968/thumbnail.jp
Alien Registration- Gervais, Marie C. (Dixfield, Oxford County)
https://digitalmaine.com/alien_docs/15684/thumbnail.jp
Light-Cone Quantization of the Liouville Model
We present the quantization of the Liouville model defined in light-cone
coordinates in (1,1) signature space. We take advantage of the representation
of the Liouville field by the free field of the Backl\"{u}nd transformation and
adapt the approch by Braaten, Curtright and Thorn.
Quantum operators of the Liouville field ,
, , are constructed consistently in
terms of the free field. The Liouville model field theory space is found to be
restricted to the sector with field momentum , , which
is a closed subspace for the Liouville theory operator algebra.Comment: 16 p, EFI-92-6
Berry Phase in Cuprate Superconductors
Geometrical Berry phase is recognized as having profound implications for the
properties of electronic systems. Over the last decade, Berry phase has been
essential to our understanding of new materials, including graphene and
topological insulators. The Berry phase can be accessed via its contribution to
the phase mismatch in quantum oscillation experiments, where electrons
accumulate a phase as they traverse closed cyclotron orbits in momentum space.
The high-temperature cuprate superconductors are a class of materials where the
Berry phase is thus far unknown despite the large body of existing quantum
oscillations data. In this report we present a systematic Berry phase analysis
of Shubnikov - de Haas measurements on the hole-doped cuprates
YBaCuO, YBaCuO, HgBaCuO, and the
electron-doped cuprate NdCeCuO. For the hole-doped materials, a
trivial Berry phase of 0 mod is systematically observed whereas the
electron-doped NdCeCuO exhibits a significant non-zero Berry
phase. These observations set constraints on the nature of the high-field
normal state of the cuprates and points towards contrasting behaviour between
hole-doped and electron-doped materials. We discuss this difference in light of
recent developments related to charge density-wave and broken time-reversal
symmetry states.Comment: new version with added supplementary informatio
Phase Structure of the O(n) Model on a Random Lattice for n>2
We show that coarse graining arguments invented for the analysis of
multi-spin systems on a randomly triangulated surface apply also to the O(n)
model on a random lattice. These arguments imply that if the model has a
critical point with diverging string susceptibility, then either \g=+1/2 or
there exists a dual critical point with negative string susceptibility
exponent, \g', related to \g by \g=\g'/(\g'-1). Exploiting the exact solution
of the O(n) model on a random lattice we show that both situations are realized
for n>2 and that the possible dual pairs of string susceptibility exponents are
given by (\g',\g)=(-1/m,1/(m+1)), m=2,3,.... We also show that at the critical
points with positive string susceptibility exponent the average number of loops
on the surface diverges while the average length of a single loop stays finite.Comment: 18 pages, LaTeX file, two eps-figure
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