1,620 research outputs found
Construction of Field Algebras with Quantum Symmetry from Local Observables
It has been discussed earlier that ( weak quasi-) quantum groups allow for
conventional interpretation as internal symmetries in local quantum theory.
From general arguments and explicit examples their consistency with (braid-)
statistics and locality was established. This work addresses to the
reconstruction of quantum symmetries and algebras of field operators. For every
algebra \A of observables satisfying certain standard assumptions, an
appropriate quantum symmetry is found. Field operators are obtained which act
on a positive definite Hilbert space of states and transform covariantly under
the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation
relations, these fields are demonstrated to obey local braid relation.Comment: 50 pages, HUTMP 93-B33
Quantisation of the SU(N) WZW Model at Level
The quantisation of the Wess-Zumino-Witten model on a circle is discussed in
the case of at level . The quantum commutation of the chiral vertex
operators is described by an exchange relation with a braiding matrix, .
Using quantum consistency conditions, the braiding matrix is found explicitly
in the fundamental representation. This matrix is shown to be related to the
Racah matrix for . From calculating the four-point functions with
the Knizhnik-Zamolodchikov equations, the deformation parameter is shown to
be when the level . For , there are two
possible types of braiding, or . In the
latter case, the chiral vertex operators are constructed explicitly by
extending the free field realisation a la Frenkel-Kac and Segal. This
construction gives an explicit description of how to chirally factorise the
WZW model.Comment: DAMTP-94-42, 21 page
Quantum groups and nonabelian braiding in quantum Hall systems
Wave functions describing quasiholes and electrons in nonabelian quantum Hall
states are well known to correspond to conformal blocks of certain coset
conformal field theories. In this paper we explicitly analyse the algebraic
structure underlying the braiding properties of these conformal blocks. We
treat the electrons and the quasihole excitations as localised particles
carrying charges related to a quantum group that is determined explicitly for
the cases of interest. The quantum group description naturally allows one to
analyse the braid group representations carried by the multi-particle wave
functions. As an application, we construct the nonabelian braid group
representations which govern the exchange of quasiholes in the fractional
quantum Hall effect states that have been proposed by N. Read and E. Rezayi,
recovering the results of C. Nayak and F. Wilczek for the Pfaffian state as a
special case.Comment: 60 pages, 7 figures, LaTeX, uses AMSfont
On the Two-Point Correlation Function for the Invariant Spin One-Half Heisenberg Chain at Roots of Unity
Using tensor calculus we compute the two-point scalar operators
(TPSO), their averages on the ground-state give the two-point correlation
functions. The TPSOs are identified as elements of the Temperley-Lieb algebra
and a recurrence relation is given for them. We have not tempted to derive the
analytic expressions for the correlation functions in the general case but got
some partial results. For , all correlation functions are
(trivially) zero, for , they are related in the continuum to the
correlation functions of left-handed and right-handed Majorana fields in the
half plane coupled by the boundary condition. In the case , one
gets the correlation functions of Mittag's and Stephen's parafermions for the
three-state Potts model. A diagrammatic approach to compute correlation
functions is also presented.Comment: 19 pages, LaTeX, BONN-HE-93-3
Functional integration on two dimensional Regge geometries
By adopting the standard definition of diffeomorphisms for a Regge surface we
give an exact expression of the Liouville action both for the sphere and the
torus topology in the discretized case. The results are obtained in a general
way by choosing the unique self--adjoint extension of the Lichnerowicz operator
satisfying the Riemann--Roch relation. We also give the explicit form of the
integration measure for the conformal factor. For the sphere topology the
theory is exactly invariant under the transformations, while for the
torus topology we have exact translational and modular invariance. In the
continuum limit the results flow into the well known expressions.Comment: 36 pages, no figures, plain latex fil
Pharmacokinetics and tumor dynamics of the nanoparticle IT-101 from PET imaging and tumor histological measurements
IT-101, a cyclodextrin polymer-based nanoparticle containing camptothecin, is in clinical development for the treatment of cancer. Multiorgan pharmacokinetics and accumulation in tumor tissue of IT-101 is investigated by using PET. IT-101 is modified through the attachment of a 1,4,7,10-tetraazacyclododecane-1,4,7-Tris-acetic acid ligand to bind ^(64)Cu^(2+). This modification does not affect the particle size and minimally affects the surface charge of the resulting nanoparticles. PET data from ^(64)Cu-labeled IT-101 are used to quantify the in vivo biodistribution in mice bearing Neuro2A s.c. tumors. The ^(64)Cu-labeled IT-101 displays a biphasic plasma elimination. Approximately 8% of the injected dose is rapidly cleared as a low-molecular-weight fraction through the kidneys. The remaining material circulates in plasma with a terminal half-life of 13.3 h. Steadily increasing concentrations, up to 11% injected dose per cm^3, are observed in the tumor over 24 h, higher than any other tissue at that time. A 3-compartment model is used to determine vascular permeability and nanoparticle retention in tumors, and is able to accurately represent the experimental data. The calculated tumor vascular permeability indicates that the majority of nanoparticles stay intact in circulation and do not disassemble into individual polymer strands. A key assumption to modeling the tumor dynamics is that there is a “sink” for the nanoparticles within the tumor. Histological measurements using confocal microscopy show that IT-101 localizes within tumor cells and provides the sink in the tumor for the nanoparticles
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
- …