2,915 research outputs found
Gauge theory on nonassociative spaces
We show how to do gauge theory on the octonions and other nonassociative
algebras such as `fuzzy ' models proposed in string theory. We use the
theory of quasialgebras obtained by cochain twist introduced previously. The
gauge theory in this case is twisting-equivalent to usual gauge theory on the
underlying classical space. We give a general U(1)-Yang-Mills example for any
quasi-algebra and a full description of the moduli space of flat connections in
this theory for the cube and hence for the octonions. We also obtain
further results about the octonions themselves; an explicit Moyal-product
description of them as a nonassociative quantisation of functions on the cube,
and a characterisation of their cochain twist as invariant under Fourier
transform.Comment: 24 pages latex, two .eps figure
Braided Cyclic Cocycles and Non-Associative Geometry
We use monoidal category methods to study the noncommutative geometry of
nonassociative algebras obtained by a Drinfeld-type cochain twist. These are
the so-called quasialgebras and include the octonions as braided-commutative
but nonassociative coordinate rings, as well as quasialgebra versions
\CC_{q}(G) of the standard q-deformation quantum groups. We introduce the
notion of ribbon algebras in the category, which are algebras equipped with a
suitable generalised automorphism , and obtain the required
generalisation of cyclic cohomology. We show that this \emph{braided cyclic
cocohomology} is invariant under a cochain twist. We also extend to our
generalisation the relation between cyclic cohomology and differential calculus
on the ribbon quasialgebra. The paper includes differential calculus and cyclic
cocycles on the octonions as a finite nonassociative geometry, as well as the
algebraic noncommutative torus as an associative example.Comment: 36 pages latex, 9 figure
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
Bicrossproduct structure of the null-plane quantum Poincare algebra
A nonlinear change of basis allows to show that the non-standard quantum
deformation of the (3+1) Poincare algebra has a bicrossproduct structure.
Quantum universal R-matrix, Pauli-Lubanski and mass operators are presented in
the new basis.Comment: 7 pages, LaTe
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
Single-, Dual- and Triple-band Frequency Reconfigurable Antenna
The paper presents a frequency reconfigurable slot dipole antenna. The antenna is capable of being switched between single-band, dual-band or triple-band operation. The antenna incorporates three pairs of pin-diodes which are located within the dipole arms. The antenna was designed to operate at 2.4 GHz, 3.5 GHz and 5.2 GHz using the aid of CST Microwave Studio. The average measured gains are 1.54, 2.92 and 1.89 dBi for low, mid and high band respectively. A prototype was then constructed in order to verify the performance of the device. A good level of agreement was observed between simulation and measurement
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.
Spectral noncommutative geometry and quantization: a simple example
We explore the relation between noncommutative geometry, in the spectral
triple formulation, and quantum mechanics. To this aim, we consider a dynamical
theory of a noncommutative geometry defined by a spectral triple, and study its
quantization. In particular, we consider a simple model based on a finite
dimensional spectral triple (A, H, D), which mimics certain aspects of the
spectral formulation of general relativity. We find the physical phase space,
which is the space of the onshell Dirac operators compatible with A and H. We
define a natural symplectic structure over this phase space and construct the
corresponding quantum theory using a covariant canonical quantization approach.
We show that the Connes distance between certain two states over the algebra A
(two ``spacetime points''), which is an arbitrary positive number in the
classical noncommutative geometry, turns out to be discrete in the quantum
theory, and we compute its spectrum. The quantum states of the noncommutative
geometry form a Hilbert space K. D is promoted to an operator *D on the direct
product *H of H and K. The triple (A, *H, *D) can be viewed as the quantization
of the family of the triples (A, H, D).Comment: 7 pages, no figure
Unbraiding the braided tensor product
We show that the braided tensor product algebra
of two module algebras of a quasitriangular Hopf algebra is
equal to the ordinary tensor product algebra of with a subalgebra of
isomorphic to , provided there exists a
realization of within . In other words, under this assumption we
construct a transformation of generators which `decouples' (i.e.
makes them commuting). We apply the theorem to the braided tensor product
algebras of two or more quantum group covariant quantum spaces, deformed
Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page
Multiband monopole antenna for mobile applications
â In this paper, a multiband monopole antenna has
been proposed for mobile applications. The monopole antenna
has simple structure with a physical size of 15 cm Ă 7 cm. The
antenna consists of monopole shape loaded by a set of folded
arms with a varying length which lead to a better impedance
matching result and multiband performance. The simulated
results show that the proposed antenna provide multiband
frequency operation of 0.8 GHz, 1.8 GHz 2.1 GHz, 2.6 GHz
and 3.5 GHz which covers the range from 0 to 4 GHz. The
antenna is designed to operate at sub-6 GHz which proposed as
lower frequency band to deliver 5G in early stage. The
designed antenna has been fabricated and measured to validate
the simulated results. RF Coaxial U.FL Connector was used as
the port connector. The measurement results agrees well with
the simulated ones for all frequency bands
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