Dirac structures and Dixmier-Douady bundles

A Dirac structure on a vector bundle V is a maximal isotropic subbundle E of the direct sum of V with its dual. We show how to associate to any Dirac structure a Dixmier-Douady bundle A, that is, a Z/2Z-graded bundle of C*-algebras with typical fiber the compact operators on a Hilbert space. The construction has good functorial properties, relative to Morita morphisms of Dixmier-Douady bundles. As applications, we show that the `spin' Dixmier-Douady bundle over a compact, connected Lie group (as constructed by Atiyah-Segal) is multiplicative, and we obtain a canonical `twisted Spin-c-structure' on spaces with group valued moment maps.Comment: 41 page

On the Kashiwara-Vergne conjecture

Let $G$ be a connected Lie group, with Lie algebra $g$. In 1977, Duflo constructed a homomorphism of $g$-modules $Duf: S(g) -> U(g)$, which restricts to an algebra isomorphism on invariants. Kashiwara and Vergne (1978) proposed a conjecture on the Campbell-Hausdorff series, which (among other things) extends the Duflo theorem to germs of bi-invariant distributions on the Lie group $G$. The main results of the present paper are as follows. (1) Using a recent result of Torossian (2002), we establish the Kashiwara-Vergne conjecture for any Lie group $G$. (2) We give a reformulation of the Kashiwara-Vergne property in terms of Lie algebra cohomology. As a direct corollary, one obtains the algebra isomorphism $H(g,S(g)) -> H(g,U(g))$, as well as a more general statement for distributions.Comment: 18 pages, final version, to be published in Inventiones Mat

Clifford algebras and the classical dynamical Yang-Baxter equation

We describe a relationship of the classical dynamical Yang-Baxter equation with the following elementary problem for Clifford algebras: Given a vector space $V$ with quadratic form $Q_V$, how is the exponential of an element in $\wedge^2(V)$ under exterior algebra multiplication related to its exponential under Clifford multiplication

A dynamical collective calculation of supernova neutrino signals

We present the first calculations with three flavors of collective and shock wave effects for neutrino propagation in core-collapse supernovae using hydroynamical density profiles and the S matrix formalism. We explore the interplay between the neutrino-neutrino interaction and the effects of multiple resonances upon the time signal of positrons in supernova observatories. A specific signature is found for the inverted hierarchy and a large third neutrino mixing angle and we predict, in this case, a dearth of lower energy positrons in Cherenkov detectors midway through the neutrino signal and the simultaneous revelation of valuable information about the original fluxes. We show that this feature is also observable with current generation neutrino detectors at the level of several sigmas.Comment: 4 pages, 5 figure

Second bound state of PsH

The existence of a second bound state of PsH that is electronically stable and also stable against positron annihilation by the normal 2gamma and 3gamma processes is demonstrated by explicit calculation. The state can be found in the 2,4So symmetries with the two electrons in a spin triplet state. The binding energy against dissociation into the H(2p) + Ps(2p) channel was 6.06x10-4 Hartree. The dominant decay mode of the states will be radiative decay into a configuration that autoionizes or undergoes positron annihilation. The NaPs system of the same symmetry is also electronically stable with a binding energy of 1.553x10-3 Hartree with respect to the Na(3p) + Ps(2p) channel.Comment: 4 pages, 2 figures, RevTex styl

The 1/N-expansion, quantum-classical correspondence and nonclassical states generation in dissipative higher-order anharmonic oscillators

We develop a method for the determination of thecdynamics of dissipative quantum systems in the limit of large number of quanta N, based on the 1/N-expansion of Heidmann et al. [ Opt. Commun. 54, 189 (1985) ] and the quantum-classical correspondence. Using this method, we find analytically the dynamics of nonclassical states generation in the higher-order anharmonic dissipative oscillators for an arbitrary temperature of a reservoir. We show that the quantum correction to the classical motion increases with time quadratically up to some maximal value, which is dependent on the degree of nonlinearity and a damping constant, and then it decreases. Similarities and differences with the corresponding behavior of the quantum corrections to the classical motion in the Hamiltonian chaotic systems are discussed. We also compare our results obtained for some limiting cases with the results obtained by using other semiclassical tools and discuss the conditions for validity of our approach.Comment: 15 pages, RevTEX (EPSF-style), 3 figs. Replaced with final version (stylistic corrections

New Test of Supernova Electron Neutrino Emission using Sudbury Neutrino Observatory Sensitivity to the Diffuse Supernova Neutrino Background

Supernovae are rare nearby, but they are not rare in the Universe, and all past core-collapse supernovae contributed to the Diffuse Supernova Neutrino Background (DSNB), for which the near-term detection prospects are very good. The Super-Kamiokande limit on the DSNB electron {\it antineutrino} flux, $\phi(E_\nu > 19.3 {\rm MeV}) < 1.2$ cm$^{-2}$ s$^{-1}$, is just above the range of recent theoretical predictions based on the measured star formation rate history. We show that the Sudbury Neutrino Observatory should be able to test the corresponding DSNB electron {\it neutrino} flux with a sensitivity as low as $\phi(22.5 < E_\nu < 32.5 {\rm MeV}) \simeq 6$ cm$^{-2}$ s$^{-1}$, improving the existing Mont Blanc limit by about three orders of magnitude. While conventional supernova models predict comparable electron neutrino and antineutrino fluxes, it is often considered that the first (and forward-directed) SN 1987A event in the Kamiokande-II detector should be attributed to electron-neutrino scattering with an electron, which would require a substantially enhanced electron neutrino flux. We show that with the required enhancements in either the burst or thermal phase $\nu_e$ fluxes, the DSNB electron neutrino flux would generally be detectable in the Sudbury Neutrino Observatory. A direct experimental test could then resolve one of the enduring mysteries of SN 1987A: whether the first Kamiokande-II event reveals a serious misunderstanding of supernova physics, or was simply an unlikely statistical fluctuation. Thus the electron neutrino sensitivity of the Sudbury Neutrino Observatory is an important complement to the electron antineutrino sensitivity of Super-Kamiokande in the quest to understand the DSNB.Comment: 10 pages, 3 figure