Homomorphisms of quantum groups

In this article, we study several equivalent notions of homomorphism between locally compact quantum groups compatible with duality. In particular, we show that our homomorphisms are equivalent to functors between the respective categories of coactions. We lift the reduced bicharacter to universal quantum groups for any locally compact quantum group defined by a modular multiplicative unitary, without assuming Haar weights. We work in the general setting of modular multiplicative unitaries

Measurement of the Higgs Boson Mass with a Linear e+e- Collider

The potential of a linear e+e- collider operated at a centre-of-mass energy of 350 GeV is studied for the measurement of the Higgs boson mass. An integrated luminosity of 500 fb-1 is assumed. For Higgs boson masses of 120, 150 and 180 GeV the uncertainty on the Higgs boson mass measurement is estimated to be 40, 65 and 70 MeV, respectively. The effects of beam related systematics, namely a bias in the beam energy measurement, the beam energy spread and the luminosity spectrum due to beamstrahlung, on the precision of the Higgs boson mass measurement are investigated. In order to keep the systematic uncertainty on the Higgs boson mass well below the level of the statistical error, the beam energy measurement must be controlled with a relative precision better than 10-4.Comment: 19 pages, 10 Figure

Localisation and mass generation for non-Abelian gauge fields

It has been suggested recently that in the presence of suitably "warped" extra dimensions, the low-energy limit of pure gauge field theory may contain massive elementary vector bosons localised on a "brane", but no elementary Higgs scalars. We provide non-perturbative evidence in favour of this conjecture through numerical lattice measurements of the static quark-antiquark force of pure SU(2) gauge theory in three dimensions, of which one is warped. We consider also warpings leading to massless localised vector bosons, and again find evidence supporting the perturbative prediction, even though the gauge coupling diverges far from the brane in this case.Comment: 27 pages; small clarifications adde

Equivariant comparison of quantum homogeneous spaces

We prove the deformation invariance of the quantum homogeneous spaces of the q-deformation of simply connected simple compact Lie groups over the Poisson-Lie quantum subgroups, in the equivariant KK-theory with respect to the translation action by maximal tori. This extends a result of Neshveyev-Tuset to the equivariant setting. As applications, we prove the ring isomorphism of the K-group of Gq with respect to the coproduct of C(Gq), and an analogue of the Borsuk-Ulam theorem for quantum spheres.Comment: 21 page

Quantum teardrops

Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops are described in detail. In particular the presentation of the coordinate algebra of the quantum teardrop in terms of generators and relations and classification of irreducible *-representations are derived. The algebras are then analysed from the point of view of Hopf-Galois theory or the theory of quantum principal bundles. Fredholm modules and associated traces are constructed. C*-algebras of continuous functions on quantum weighted projective lines are described and their K-groups computed.Comment: 18 page

Signals that stop the rot : regulation of secondary metabolite defences in cereals

Plants accumulate a vast arsenal of chemically diverse secondary metabolites for defence against pathogens. This review will focus on the signal transduction and regulation of defence secondary metabolite production in five food security cereal crops: maize, rice, wheat, sorghum and oats. Recent research advances in this field have revealed novel processes and chemistry in these monocots that make this a rich field for future research.The National Research Foundation (NRF) and the Genomics Research Institute at the University of Pretoria (UP), South Africa.http://www.elsevier.com/locate/pmpp2017-04-30hb2016Forestry and Agricultural Biotechnology Institute (FABI)Plant Scienc

Effective gauge theories on domain walls via bulk confinement?

We study with lattice techniques the localisation of gauge fields on domain wall defects in 2+1 dimensions, following a scenario originally proposed by Dvali and Shifman for 3+1 dimensions, based on confining dynamics in the bulk. We find that a localised gauge zero-mode does exist, if the domain wall is wide enough compared with the confinement scale in the bulk. The range of applicability of the corresponding low-energy effective theory is determined by the mass gap to the higher modes. For a wide domain wall, this mass gap is set by ``Kaluza--Klein modes'' as determined by the width. It is pointed out that in this regime the dynamical energy scales generated by the interactions of the localised zero-modes are in fact higher than the mass gap. Therefore, at least in 2+1 dimensions, the zero-modes alone do not form a low-energy effective gauge theory of a traditional type. Finally, we discuss how the situation is expected to change in going to 3+1 dimensions.Comment: 24 pages. v2: published versio

Geometric Strategy for the Optimal Quantum Search

We explore quantum search from the geometric viewpoint of a complex projective space $CP$, a space of rays. First, we show that the optimal quantum search can be geometrically identified with the shortest path along the geodesic joining a target state, an element of the computational basis, and such an initial state as overlaps equally, up to phases, with all the elements of the computational basis. Second, we calculate the entanglement through the algorithm for any number of qubits $n$ as the minimum Fubini-Study distance to the submanifold formed by separable states in Segre embedding, and find that entanglement is used almost maximally for large $n$. The computational time seems to be optimized by the dynamics as the geodesic, running across entangled states away from the submanifold of separable states, rather than the amount of entanglement itself.Comment: revtex, 10 pages, 7 eps figures, uses psfrag packag

An evaluation of the endophytic colonies present in pathogenic and non-pathogenic Vanguerieae using electron microscopy

Fadogia homblei, Pavetta harborii, Pavetta schumanniana, Vangueria pygmaea (=Pachystigma pygmaeum), Vangueria latifolia (=Pachystigma latifolium) and Vangueria thamnus (=Pachystigma thamnus) all induce one of the most important cardiotoxicoses of domestic ruminants in southern Africa, causing the sickness gousiekte. All the plants which cause gousiekte have previously been shown to contain bacterial endophytes. However, in this study other plants within the Vanguerieae tribe that have not been reported to cause gousiekte; namely Vangueria infausta, Vangueria macrocalyx and Vangueria madagascariensis, have now been shown to also contain endophytes within the inter-cellular spaces of the leaves. The disease gousiekte is difficult to characterise due to fluctuations in plant toxicity. The majority of reported cases of gousiekte poisoning are at the beginning of the growing season; and thus the plants are thought to be more toxic at this time. By using both transmission and scanning electron microscopy the endophytes within these Vanguerieae plants were compared visually. Using the plant reported most often for gousiekte poisoning, V. pygmaea, a basic seasonal comparison of the presence of endophytes was done. It was found that the bacterial endophyte colonies were most abundant during the spring season.The National Research Foundation of South Africa and Professor T. Coutinho.http:// www.elsevier.com/ locate/sajbam201

Transport Properties of the Quark-Gluon Plasma -- A Lattice QCD Perspective

Transport properties of a thermal medium determine how its conserved charge densities (for instance the electric charge, energy or momentum) evolve as a function of time and eventually relax back to their equilibrium values. Here the transport properties of the quark-gluon plasma are reviewed from a theoretical perspective. The latter play a key role in the description of heavy-ion collisions, and are an important ingredient in constraining particle production processes in the early universe. We place particular emphasis on lattice QCD calculations of conserved current correlators. These Euclidean correlators are related by an integral transform to spectral functions, whose small-frequency form determines the transport properties via Kubo formulae. The universal hydrodynamic predictions for the small-frequency pole structure of spectral functions are summarized. The viability of a quasiparticle description implies the presence of additional characteristic features in the spectral functions. These features are in stark contrast with the functional form that is found in strongly coupled plasmas via the gauge/gravity duality. A central goal is therefore to determine which of these dynamical regimes the quark-gluon plasma is qualitatively closer to as a function of temperature. We review the analysis of lattice correlators in relation to transport properties, and tentatively estimate what computational effort is required to make decisive progress in this field.Comment: 54 pages, 37 figures, review written for EPJA and APPN; one parag. added end of section 3.4, and one at the end of section 3.2.2; some Refs. added, and some other minor change