Muon capture on light nuclei

This work investigates the muon capture reactions 2H(\mu^-,\nu_\mu)nn and 3He(\mu^-,\nu_\mu)3H and the contribution to their total capture rates arising from the axial two-body currents obtained imposing the partially-conserved-axial-current (PCAC) hypothesis. The initial and final A=2 and 3 nuclear wave functions are obtained from the Argonne v_{18} two-nucleon potential, in combination with the Urbana IX three-nucleon potential in the case of A=3. The weak current consists of vector and axial components derived in chiral effective field theory. The low-energy constant entering the vector (axial) component is determined by reproducting the isovector combination of the trinucleon magnetic moment (Gamow-Teller matrix element of tritium beta-decay). The total capture rates are 393.1(8) s^{-1} for A=2 and 1488(9) s^{-1} for A=3, where the uncertainties arise from the adopted fitting procedure.Comment: 6 pages, submitted to Few-Body Sys

Closedness of star products and cohomologies

We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.Comment: 16 page

A Short Survey of Noncommutative Geometry

We give a survey of selected topics in noncommutative geometry, with some emphasis on those directly related to physics, including our recent work with Dirk Kreimer on renormalization and the Riemann-Hilbert problem. We discuss at length two issues. The first is the relevance of the paradigm of geometric space, based on spectral considerations, which is central in the theory. As a simple illustration of the spectral formulation of geometry in the ordinary commutative case, we give a polynomial equation for geometries on the four dimensional sphere with fixed volume. The equation involves an idempotent e, playing the role of the instanton, and the Dirac operator D. It expresses the gamma five matrix as the pairing between the operator theoretic chern characters of e and D. It is of degree five in the idempotent and four in the Dirac operator which only appears through its commutant with the idempotent. It determines both the sphere and all its metrics with fixed volume form. We also show using the noncommutative analogue of the Polyakov action, how to obtain the noncommutative metric (in spectral form) on the noncommutative tori from the formal naive metric. We conclude on some questions related to string theory.Comment: Invited lecture for JMP 2000, 45

Formality theorems for Hochschild complexes and their applications

We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.Comment: Submitted to proceedings of Poisson 200

Oscilatory modules

Developing the ideas of Bressler and Soibelman and of Karabegov, we introduce a notion of an oscillatory module on a symplectic manifold which is a sheaf of modules over the sheaf of deformation quantization algebras with an additional structure. We compare the category of oscillatory modules on a torus to the Fukaya category as computed by Polishchuk and Zaslow.Comment: To appear in the proceedings of Moshe Flato Memorial Conference, November, 2008, Ben Gurion Universit

Cyclic homology and the Macdonald conjectures

Let A+(k) denote the ring ℂ[ t ]/ t k+1 and let G be a reductive complex Lie algebra with exponents m 1 , ..., m n . This paper concerns the Lie algebra cohomology of G ⊗ A + ( k ) considered as a bigraded algebra (here one of the gradings is homological degree and the other, which we call weight , is inherited from the obvious grading of G ⊗ A + ( k )). We conjecture that this Lie algebra cohomology is an exterior algebra with k +1 generators of homological degree 2 m s +1 for s =1,2, ..., n . Of these k +1 generators of degree 2 m s +1, one has weight 0 and the others have weights ( k +1) m s +t for t =1,2, ..., k .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46617/1/222_2005_Article_BF01391498.pd

On the Internal Structure of Relativistic Jets

A magnetohydrodynamic model is constructed for a cylindrical jet immersed in an external uniform magnetic field. It is shown that, as in the force-free case, the total electric current within the jet can be zero. The particle energetics and the magnetic field structure are determined in a self-consistent way; all jet parameters depend on the physical conditions in the external medium. In particular, we show that a region with subsonic flow can exist in the central jet regions. In actual relativistic jets, most of the energy is transferred by the electromagnetic field only when the magnetization parameter is sufficiently large, $\sigma>10^6$. We also show that, in general, the well-known solution with a central core, $B_z = B_0/(1+\varpi^2/\varpi_c^2)$, can not be realized in the presence of an external medium.Comment: 19 pages, 2 figure