Linking numbers in local quantum field theory

Linking numbers appear in local quantum field theory in the presence of tensor fields, which are closed two-forms on Minkowski space. Given any pair of such fields, it is shown that the commutator of the corresponding intrinsic (gauge-invariant) vector potentials, integrated about spacelike separated, spatial loops, are elements of the center of the algebra of all local fields. Moreover, these commutators are proportional to the linking numbers of the underlying loops. If the commutators are different from zero, the underlying two-forms are not exact (i.e. there do not exist local vector potentials for them). The theory then necessarily contains massless particles. A prominent example of this kind, due to J.E. Roberts, is given by the free electromagnetic field and its Hodge dual. Further examples with more complex mass spectrum are presented in this article.

     

Limit on right handed weak coupling parameters from inelastic neutrino interactions

Right handed weak quark currents coupled to the usual left handed weak lepton current would be seen in inclusive antineutrino scattering on nuclei as a contribution at largey with the quark (not antiquark) structure function. We do not see such a term, and can therefore put an upper limit on the relative strengths of such right handed currents: \(\varrho ^2 = \frac{{\sigma _R }}{{\sigma _L }}< 0.009\) , 90% confidence. This measurement puts limits on the mixing angle of left-right symmetric models. In distinction to similar limits derived from muon decay or β decay, our limits are also valid if the right handed neutrino is heavy.     

Lifetimes of charged and neutralD mesons

We have measured the lifetimes of hadronically produced charged and neutralD mesons using silicon microstrip detectors and an active silicon target in the NA32 spectrometer at the CERN SPS. We obtainτ _D± = (10.9± _1.5 ^1.9 )·10^?13s andτ _D ^(?)10 = (4.2±0.5)·10^?13s based on 59 and 90 fully reconstructed decays respectively, giving a ratioτ _D±/τ _D ^(?)10 of 2.6 ±0.5.     

Thrust performance of unsteady propulsors using a novel measurement system,and corresponding wake patterns

An apparatus is described for the measurement of unsteady thrust and propulsive efficiency produced by biologically inspired oscillating hydrodynamic propulsors. Force measurement is achieved using a strain-gauge-based force transducer, augmented with a lever to amplify or attenuate the applied force and control the measurement sensitivity and natural frequency of vibration. The lever can be used to tune the system to a specific application and it is shown that, using the lever, the stiffness can be made to increase more rapidly than the measurement sensitivity decreases. Efficiency is computed from measurements of the time-averaged power imparted to the fluid. The apparatus is applied to two different propulsors, demonstrating the versatility of the system; wake visualizations are examined, which provide insight into the physical mechanisms of efficient propulsion.

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Elliptic Curves Suitable for Pairing Based Cryptography

For pairing based cryptography we need elliptic curves defined over finite fields whose group order is divisible by some prime with where k is relatively small. In Barreto et al. and Dupont et al. [Proceedings of the Third Workshop on Security in Communication Networks (SCN 2002), LNCS, 2576, 2003; Building curves with arbitrary small Mov degree over finite fields, Preprint, 2002], algorithms for the construction of ordinary elliptic curves over prime fields with arbitrary embedding degree k are given. Unfortunately, p is of size .We give a method to generate ordinary elliptic curves over prime fields with p significantly less than which also works for arbitrary k. For a fixed embedding degree k, the new algorithm yields curves with where or depending on k. For special values of k even better results are obtained.We present several examples. In particular, we found some curves where is a prime of small Hamming weight resp. with a small addition chain.AMS classification: 14H52, 14G50     

On the action of Ariki–Koike algebras on tensor space

The action of the Ariki–Koike algebra on tensor space is used to show that the Ariki–Koike algebra is isomorphic to a direct sum of matrix rings over tensor products over smaller Ariki–Koike algebras. As an application we get Schur–Weyl duality for the action of the Ariki–Koike algebra and the Levi subalgebra of the q-Schur algebra when separation conditions holds.