The Differential Geometry of Fedosov’s Quantization
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: 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: 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: 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: 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: First observation of the sigma(*+)(c) baryon and a new measurement of the sigma(*+)(c) mass.
abstract: Using data recorded with the CLEO II and CLEO II.V detector configurations at the Cornell Electron Storage Rings, we report the first observation and mass measurement of the Sigma(*+)(c) charmed baryon, and an updated measurement of the mass of the Sigma(+)(c) baryon. We find M(Sigma(*+)(c))-M(Lambda(+)(c)) = (231.0+/-1.1+/-2.0) MeV, and M(Sigma(+)(c))-M(Lambda(+)(c)) = (166.4+/-0.2+/-0.3) MeV, where the errors are statistical and systematic, respectively.

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: Measurements of the meson-photon transition form factors of light pseudoscalar mesons at large momentum transfer
abstract: Using the CLEO II detector, we have measured the differential cross sections for exclusive two-photon production of light pseudoscalar mesons {pi}{sup 0}, {eta}, and {eta}{prime}. From our measurements we have obtained the form factors associated with the electromagnetic transitions {gamma}*{gamma} {yields} meson. We have measured these form factors in the momentum transfer ranges from 1.5 to 9, 20, and 30 GeV2 for {pi}{sup 0}, {eta}, and {eta}{prime}, respectively, and have made comparisons to various theoretical predictions.

title: Observation of the Hadronic transitions chi(b1,2)(2P)-->omegaUpsilon(1S).
abstract: The CLEO Collaboration has made the first observations of hadronic transitions among bottomonium (bbmacr;) states other than the dipion transitions among Upsilon(nS) states. In our study of Upsilon(3S) decays, we find a significant signal for Upsilon(3S)-->gammaomegaUpsilon(1S) that is consistent with radiative decays Upsilon(3S)-->gammachi(b1,2)(2P), followed by chi(b1,2)(2P)-->omegaUpsilon(1S). The branching ratios we obtain are B[chi(b1)(2P)-->omegaUpsilon(1S)]=(1.63(+0.35+0.16)(-0.31-0.15))% and B[chi(b2)(2P)-->omegaUpsilon(1S)]=(1.10(+0.32+0.11)(-0.28-0.10))%, in which the first error is statistical and the second is systematic.

title: Measurement of CP asymmetries in $B^0 \to K_s 0 \pi^0 \pi^0$ decays
abstract: We present a preliminary measurement of the time-dependent CP asymmetry for the neutral B-meson decay into the CP = +1 final state KS pi0 pi0, with KS-> pi+ pi- and pi0-> gamma gamma. We use a sample of approximately 227 million B-meson pairs recorded at the Y(4S) resonance by the BaBar detector at the PEP-II B-Factory at SLAC. From a maximum likelihood fit we extract the mixing-induced CP-violation parameter S = 0.84 +/- 0.71(stat} +/- 0.08{syst) and the direct CP-violation parameter C = 0.27 +/- 0.52(stat) +/- 0.13(syst}, where the first uncertainty is statistical and the second systematic.