A universal phase space for particles in Yang-Mills fields
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: Noncommutative Geometry and Geometric Quantization

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: Poisson geometry with a 3 form background
abstract: We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these "twisted" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of 2-forms acts on twisted Poisson structures and permits them to be seen as glued from ordinary Poisson structures defined on local patches. We conclude with remarks on deformation quantization and twisted symplectic groupoids.

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: Geometry of the transport equation in multicomponent WKB approximations
abstract: Although the WKB approximation for multicomponent systems has been intensively studied in the literature, its geometric and global aspects are much less well understood than in the scalar case. In this paper we give a completely geometric derivation of the transport equation, without using local sections and without assuming complete diagonalizability of the matrix valued principal symbol, or triviality of its eigenbundles. The term (unnamed in the previous literature) appearing in the transport equation in addition to the covariant derivative with respect to a natural projected connection is a tensor, independent of the choice of any sections. We give a goemetric interpretation of this tensor, involving the contraction of the curvature of the eigenbundle and an analog of the second fundamental form with the Poisson tensor in phase space. In the non-degenerate case this term may be rewritten in an even simpler geometric form. Finally, we discuss obstructions to the existence of WKB states and give a geometric description of the quantization condition for WKB states for a non-degenerate eigenvalue-function.

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: Of Symmetries and Factories, Matter and Antimatter
abstract: An elusive subatomic particle called the B decays in a way that violates a fundamental symmetry of nature. Physicists hope to study this decay pattern at a "B Factory," as learning its secrets may explain why there is more matter than antimatter in the universe today.

title: Study of $B^0$ (anti-B0) $\to \pi^0 \pi^0$, $B^\pm \to \pi^\pm \pi^0$ and $B^\pm \to K^\pm \pi^0$ decays

title: Measurement of the $B^\pm \to \rho^\pm \pi^0$ branching fraction and direct CP asymmetry
abstract: An improved measurement of the process B+- --> rho+- pi0 is presented. The data sample of 211/fb comprises 232 million Y(4S) --> BBbar decays collected with the BaBar detector at the PEP-II asymmetric-energy B Factory at SLAC. The yield and CP asymmetry are calculated using an extended maximum likelihood fitting method. The branching fraction and asymmetry are found to be BR(B+- --> rho+- pi0) = [10.0 +- 1.4 (stat) +- 0.9 (syst)]x 10^-6 and Acp(B+- --> rho+- pi0) = -0.01 +- 0.13 (stat) +- 0.02 (syst), superseding previous measurements. The statistical significance of the branching fraction is calculated to be 8.7sigma.

title: First measurement of Gamma (D(s)+ ---> mu+ neutrino) / gamma (D(s)+ ---> phi pi+)