Reflections on the evolution of physical theories

Conclusion Let me come back to the successes of the Poincaré group in particle physics. This is a group with ten generators. The translation generators are responsible for the energy-momentum conservation laws, the rotation generators of the conservation of angular momentum, and the boost generators of the conservation ofinitial position. If positions are slightly different from the ones described by Minkowski space, it means that we have to change slightly the notion of boosts. If we remember that boosts were questionable in Minkowski space (see Section 9), we are not surprised. We are naturally led to a deformation of the Poincaré group which would preserve translations and rotations [such a deformation has been proposed by Lukierskiet al. (n.d.)]. By duality, small changes at short distances must correspond to small changes in large momenta. The fact that cutoffs for momenta are involved in QED is perhaps related to a noncommutative structure for our space. With such a structure, making the size of an electron go to zero is meaningless and consequently the difficulty of an electron with infinite energy also becomes meaningless. A noncommutative space is probably a way to solve the difficulties mentioned in the epigraphs to this paper.     

Asymmetrische Katalysen, 39. Mitt.: Monohydrosilane in der enantioselektiven katalytischen Hydrosilylierung prochiraler Ketone

The reactivity of several monohydrosilane/complex systems in the hydrosilylation of acetophenone and benzylmethylketone was investigated. The active systems were modified by addition of optically active ligands and used as enantioselectivein-situ catalysts for the hydrosilylation of the above prochiral ketones which on hydrolysis gave -phenylethanol and -benzylethanol in up to 18% ee.

     

Théories cohomologiques

Sans résuméA Jean-Pierre Serre     

Optimal teleportation with a mixed state of two qubits

We consider a single copy of a mixed state of two qubits and derive the optimal trace-preserving local operations assisted by classical communication such as to maximize the fidelity of teleportation that can be achieved with this state. These optimal local operations turn out to be implementable by one-way communication and always yield a teleportation fidelity larger than 2/3 if the original state is entangled. This maximal achievable fidelity is an entanglement measure and turns out quantifying the minimal amount of mixing required to destroy the entanglement in a quantum state.     

Giant stress fluctuations at the jamming transition

We study the stress response to a steady imposed shear rate in a concentrated suspension of colloidal particles. We show that, in a small range of concentrations and shear rates, stress exhibits giant fluctuations. The amplitude of these fluctuations obeys a power-law behavior, up to the apparition of a new branch of flow, leading to an excess of high amplitude fluctuations which exhibit a well-defined periodicity.     

Stationary solutions for the Kac model of non-linear Boltzmann equations

We study the stationary solutions of the non-linear Kac model of spatially non-homogeneous Boltzmann equations. Firstly we find the differential systems for both the power and Laguerre moments and show that they can be obtained recursively. Secondly we explain how closed quasi-similarity solutions can exist and build explicitly the most simple one, the main difficulty being reduced to a moment problem for the scattering cross section.     

Analytic torsion and holomorphic determinant bundles

In this paper, we prove that in the case of holomorphic locally Kähler fibrations, the analytic and algebraic geometry constructions of determinant bundles for direct images coincide. We calculate the curvature of the holomorphic Hermitian connection for the Quillen metric on the determinant bundle. We study the behavior of the Quillen metric under change of metrics in the fibers, and also on the twisting vector bundles. We thus generalize the conformal anomaly formula to Kähler manifolds of arbitrary dimension. We also study the Quillen metrics on determinants associated with exact sequences of vector bundles. We prove that the Quillen metric is smooth on the Grothendieck-Knudsen-Mumford determinant for arbitrary holomorphic fibrations.