3,061 research outputs found
Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group
Braided groups and braided matrices are novel algebraic structures living in
braided or quasitensor categories. As such they are a generalization of
super-groups and super-matrices to the case of braid statistics. Here we
construct braided group versions of the standard quantum groups . They
have the same FRT generators but a matrix braided-coproduct \und\Delta
L=L\und\tens L where , and are self-dual. As an application, the
degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices
; it is a braided-commutative bialgebra in a braided category. As a
second application, we show that the quantum double D(\usl) (also known as
the `quantum Lorentz group') is the semidirect product as an algebra of two
copies of \usl, and also a semidirect product as a coalgebra if we use braid
statistics. We find various results of this type for the doubles of general
quantum groups and their semi-classical limits as doubles of the Lie algebras
of Poisson Lie groups.Comment: 45 pages. Revised (= much expanded introduction
Towards Spinfoam Cosmology
We compute the transition amplitude between coherent quantum-states of
geometry peaked on homogeneous isotropic metrics. We use the holomorphic
representations of loop quantum gravity and the
Kaminski-Kisielowski-Lewandowski generalization of the new vertex, and work at
first order in the vertex expansion, second order in the graph (multipole)
expansion, and first order in 1/volume. We show that the resulting amplitude is
in the kernel of a differential operator whose classical limit is the canonical
hamiltonian of a Friedmann-Robertson-Walker cosmology. This result is an
indication that the dynamics of loop quantum gravity defined by the new vertex
yields the Friedmann equation in the appropriate limit.Comment: 8 page
On the Fock space for nonrelativistic anyon fields and braided tensor products
We realize the physical N-anyon Hilbert spaces, introduced previously via
unitary representations of the group of diffeomorphisms of the plane, as N-fold
braided-symmetric tensor products of the 1-particle Hilbert space. This
perspective provides a convenient Fock space construction for nonrelativistic
anyon quantum fields along the more usual lines of boson and fermion fields,
but in a braided category. We see how essential physical information is thus
encoded. In particular we show how the algebraic structure of our anyonic Fock
space leads to a natural anyonic exclusion principle related to intermediate
occupation number statistics, and obtain the partition function for an
idealised gas of fixed anyonic vortices.Comment: Added some references, more explicit formulae for the discrete case
and remark on partition function. 25 pages latex, no figure
Quantisation of twistor theory by cocycle twist
We present the main ingredients of twistor theory leading up to and including
the Penrose-Ward transform in a coordinate algebra form which we can then
`quantise' by means of a functorial cocycle twist. The quantum algebras for the
conformal group, twistor space CP^3, compactified Minkowski space CMh and the
twistor correspondence space are obtained along with their canonical quantum
differential calculi, both in a local form and in a global *-algebra
formulation which even in the classical commutative case provides a useful
alternative to the formulation in terms of projective varieties. We outline how
the Penrose-Ward transform then quantises. As an example, we show that the
pull-back of the tautological bundle on CMh pulls back to the basic instanton
on S^4\subset CMh and that this observation quantises to obtain the
Connes-Landi instanton on \theta-deformed S^4 as the pull-back of the
tautological bundle on our \theta-deformed CMh. We likewise quantise the
fibration CP^3--> S^4 and use it to construct the bundle on \theta-deformed
CP^3 that maps over under the transform to the \theta-deformed instanton.Comment: 68 pages 0 figures. Significant revision now has detailed formulae
for classical and quantum CP^
Generalized exclusion and Hopf algebras
We propose a generalized oscillator algebra at the roots of unity with
generalized exclusion and we investigate the braided Hopf structure. We find
that there are two solutions: these are the generalized exclusions of the
bosonic and fermionic types. We also discuss the covariance properties of these
oscillatorsComment: 10 pages, to appear in J. Phys.
Braided structure of fractional -supersymmetry
It is shown that fractional -superspace is isomorphic to the
limit of the braided line. -supersymmetry is
identified as translational invariance along this line. The fractional
translation generator and its associated covariant derivative emerge as the
limits of the left and right derivatives from the calculus
on the braided lineComment: 8 pages, LaTeX, submitted to Proceedings of the 5th Colloquium
`Quantum groups and integrable systems', Prague, June 1996 (to appear in
Czech. J. Phys.
Cosmological constant from quantum spacetime
http://dx.doi.org/10.1103/PhysRevD.91.124028© 2015, Physical Review
A note on quantum structure constants
The Cartan-Maurer equations for any -group of the
series are given in a convenient form, which allows their direct computation
and clarifies their connection with the case. These equations, defining
the field strengths, are essential in the construction of -deformed gauge
theories. An explicit expression \om ^i\we \om^j= -\Z {ij}{kl}\om ^k\we \om^l
for the -commutations of left-invariant one-forms is found, with \Z{ij}{kl}
\om^k \we \om^l \qonelim \om^j\we\om^i.Comment: 9 pp., LaTe
Synthesis and characterization of a narrow size distribution of zinc oxide nanoparticles
Zinc oxide nanoparticles (ZnO-NPs) were synthesized via a solvothermal method in triethanolamine (TEA) media. TEA was utilized as a polymer agent to terminate the growth of ZnO-NPs. The ZnO-NPs were characterized by a number of techniques, including X-ray diffraction analysis, transition electron microscopy, and field emission electron microscopy. The ZnO-NPs prepared by the solvothermal process at 150°C for 18 hours exhibited a hexagonal (wurtzite) structure, with a crystalline size of 33 ± 2 nm, and particle size of 48 ± 7 nm. The results confirm that TEA is a suitable polymer agent to prepare homogenous ZnO-NPs
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