Reduction and quantization for singular momentum mappings
When a Hamiltonian action of Lie group on a symplectic manifold has a singular momentum mapping, the reduced manifold may not exist. Nevertheless, we may always construct a Poisson algebra which corresponds to the functions on the reduced manifold in the regular case. The ideas of geometric quantization are extended to Poisson algebras, and it is shown in an example that quantization may be carried out before or after reduction, with isomorphic results.

title: A universal phase space for particles in Yang-Mills fields
abstract: Given a principal G-bundle P over M and a Hamiltonian G-space Q, one may construct the reduced symplectic manifold (T*P x Q)0. When a connection on P is chosen, this manifold becomes a bundle over T*M with fibre Q. It is shown that this bundle is precisely the phase space constructed by Sternberg for a classical particle in a Yang-Mills field.

title: Courant Algebroids and Strongly Homotopy Lie Algebras
abstract: Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the direct sum of tangent and cotangent bundles with the bracket introduced by T. Courant for the study of Dirac structures. Within the category of Courant algebroids one can construct the doubles of Lie bialgebroids, the infinitesimal objects for Poisson groupoids. We show that Courant algebroids can be considered as strongly homotopy Lie algebras.

title: Hopfish structure and modules over irrational rotation algebras
abstract: Inspired by the group structure on $S^1/ \bbZ$, we introduce a weak hopfish structure on an irrational rotation algebra $A$ of finite Fourier series. We consider a class of simple $A$-modules defined by invertible elements, and we compute the tensor product between these modules defined by the hopfish structure. This class of simple modules turns out to generate an interesting commutative unital ring.

title: The Differential Geometry of Fedosov’s Quantization
abstract: B. Fedosov has given a simple and very natural construction of a deformation quantization for any symplectic manifold, using a flat connection on the bundle of formal Weyl algebras associated to the tangent bundle of a symplectic manifold. The connection is obtained by affinizing, nonlinearizing, and iteratively flattening a given torsion free symplectic connection. In this paper, a classical analog of Fedosov’s operations on connections is analyzed and shown to produce the usual exponential mapping of a linear connection on an ordinary manifold. A symplectic version is also analyzed. Finally, some remarks are made on the implications for deformation quantization of Fedosov’s index theorem on general symplectic manifolds.

title: Noncommutative Geometry and Geometric Quantization

title: Branching fractions in $B \to \phi$ h and search for direct CP violation in $B^\pm \to \phi K^\pm$

title: Upper Limit for J/psi ---> gamma Axion
abstract: The authors have searched with the crystal ball detector for axionlike particles in radiative J/psi decays. An upper limit on the branching ratio B(J/psi..--> gamma..+a)<1.4 x 10/sup -5/ (90% C.L.) is obtained. This result holds for long-lived, noninteracting pseudoscalar or vector particles of mass less than 1 GeV. Thus, this experiment also places stringent limits on the existence of other possible light bosons such as those arising in supersymmetric theories.

title: Singular value decomposition applied to compact binary coalescence gravitational-wave signals
abstract: We investigate the application of the singular value decomposition to compact-binary, gravitational-wave data-analysis. We find that the truncated singular value decomposition reduces the number of filters required to analyze a given region of parameter space of compact-binary coalescence waveforms by an order of magnitude with high reconstruction accuracy. We also compute an analytic expression for the expected signal loss due to the singular value decomposition truncation.

title: The search for millicharged particles at SLAC
abstract: Quantization of electric charge has been probed to a high degree of precision using a variety of experimental techniques. However, the theoretical underpinning of charge quantization has yet to be determined, leaving open the possibility that quantization is not a fundamental law of nature, and that free particles with fractional electric charge may one day be encountered. This dissertation describes a search for particles with very small (10{sup -3}e or below) electric charge, carried out at an electron accelerator (SLAC). The particles sought were assumed to be long lived or stable and to participate primarily in electromagnetic interactions. The search relied upon a large (1.3-meter) scintillation counter to detect low levels of ionization generated by relativistic fractionally charged particles produced in the collision of a 29.5-GeV electron beam with a six radiation length tungsten target. The data reveal no evidence of fractional charge, and allow for the exclusion of a portion of charge-mass parameter space spanning roughly 10{sup -7} to 10{sup 2} MeV/c{sup 2} and 10{sup -2} to 10{sup -5} e.

title: Upper limits on a stochastic background of gravitational waves.
abstract: The Laser Interferometer Gravitational-Wave Observatory has performed a third science run with much improved sensitivities of all three interferometers. We present an analysis of approximately 200 hours of data acquired during this run, used to search for a stochastic background of gravitational radiation. We place upper bounds on the energy density stored as gravitational radiation for three different spectral power laws. For the flat spectrum, our limit of omega0 < 8.4 x 10(-4) in the 69-156 Hz band is approximately 10(5) times lower than the previous result in this frequency range.