1,033 research outputs found
q-deformed Dirac Monopole With Arbitrary Charge
We construct the deformed Dirac monopole on the quantum sphere for arbitrary
charge using two different methods and show that it is a quantum principal
bundle in the sense of Brzezinski and Majid. We also give a connection and
calculate the analog of its Chern number by integrating the curvature over
.Comment: Technical modifications made on the definition of the base. A more
geometrical trivialization is used in section
Lattice Gauge Theory
We reformulate the Hamiltonian approach to lattice gauge theories such that,
at the classical level, the gauge group does not act canonically, but instead
as a Poisson-Lie group. At the quantum level, it then gets promoted to a
quantum group gauge symmetry. The theory depends on two parameters - the
deformation parameter and the lattice spacing . We show that the
system of Kogut and Susskind is recovered when , while
QCD is recovered in the continuum limit (for any ). We thus have the
possibility of having a two parameter regularization of QCD.Comment: 26 pages, LATEX fil
Quantum Principal Bundles and Corresponding Gauge Theories
A generalization of classical gauge theory is presented, in the framework of
a noncommutative-geometric formalism of quantum principal bundles over smooth
manifolds. Quantum counterparts of classical gauge bundles, and classical gauge
transformations, are introduced and investigated. A natural differential
calculus on quantum gauge bundles is constructed and analyzed. Kinematical and
dynamical properties of corresponding gauge theories are discussed.Comment: 28 pages, AMS-LaTe
Coadditive differential complexes on quantum groups and quantum spaces
A regular way to define an additive coproduct (or ``coaddition'') on the
q-deformed differential complexes is proposed for quantum groups and quantum
spaces related to the Hecke-type R-matrices. Several examples of braided
coadditive differential bialgebras (Hopf algebras) are presented.Comment: 9 page
Local Index Formula on the Equatorial Podles Sphere
We discuss spectral properties of the equatorial Podles sphere. As a
preparation we also study the `degenerate' (i.e. ) case (related to the
quantum disk). We consider two different spectral triples: one related to the
Fock representation of the Toeplitz algebra and the isopectral one. After the
identification of the smooth pre--algebra we compute the dimension
spectrum and residues. We check the nontriviality of the (noncommutative) Chern
character of the associated Fredholm modules by computing the pairing with the
fundamental projector of the -algebra (the nontrivial generator of the
-group) as well as the pairing with the -analogue of the Bott
projector. Finally, we show that the local index formula is trivially
satisfied.Comment: 18 pages, no figures; minor correction
Iron, silicate, and light co-limitation of three Southern Ocean diatom species
The effect of combined iron, silicate, and light co-limitation was investigated in the three diatom species Actinocyclus sp. Ehrenberg, Chaetoceros dichaeta Ehrenberg, and Chaetoceros debilis Cleve, isolated from the Southern Ocean (SO). Growth of all species was co-limited by iron and silicate, reflected in a significant increase in the number of cell divisions compared to the control. Lowest relative Si uptake and drastic frustule malformation was found under iron and silicate co-limitation in C. dichaeta, while Si limitation in general caused cell elongation in both Chaetoceros species. Higher light intensities similar to SO surface conditions showed a negative impact on growth of C. dichaeta and Actinocyclus sp. and no effect on C. debilis. This is in contrast to the assumed light limitation of SO diatoms due to deep wind driven mixing. Our results suggest that growth and species composition of Southern Ocean diatoms is influenced by a sensitive interaction of the abiotic factors, iron, silicate, and light
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