120014189
Fat bundles and symplectic manifolds
A fat bundle is, roughly speaking, a bundle which has a lot of curvature, as opposed to a flat bundle, which has none. (The precise definition is given in Section 1.) For example, a bundle with structure group S’ is fat if it has a connection whose curvature is a symplectic structure on the base. The notion of fat bundle arises naturally from the study of riemannian fibre bundles with totally geodesic fibres. Positivity of certain sectional curvatures turns out to be equivalent to fatness of the connection determined by the orthogonal complements to the fibres. It was for this reason that fat bundles were introduced in a manuscript written at MIT in 1968 and circulated informally [20]. (The term unj7at used in that manuscript to mean fat is rather lacking in euphony; it is also slightly misleading, since a bundle which is not flat might not be unflat either-most bundles are somewhere in between.) Some of the results in this paper are taken from the 1968 manuscript, in particular Lemma 3.1, Theorem 4.1 and its corollaries, Theorem 6.1, and Theorem 7.2, but there are substantial additions as well. Using an idea of Sternberg, we show in Section 3 how to construct symplectic manifolds out of any fat bundle, using coadjoint orbits of the structure group; we then continue the discussion by using an idea of Thurston [ 181 to show that, whatever the connection, it is often possible to put a symplectic structure on the total space of a bundle whose tibres and base are symplectic. (In particular, it is sufficient that the bundle be compact and have simply connected fibres.) A problem which was posed and partially solved in [20] was to determine the fat 3-sphere bundles over S4. This problem has just been solved by Derdziriski and Rigas [7]-there is only the Hopf tibration S3 + S’ + S4. Their solution (see Section 7) uses ideas generated by the recent revival of interest in 4-dimensional riemarmian geometry [2] centered around the notion of self-duality. Several important contributions to the theory of fat bundles have been
17756587
Poisson geometry with a 3 form background
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.
121794904
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.
15329636
Hopfish structure and modules over irrational rotation algebras
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.
17256168
Courant Algebroids and Strongly Homotopy Lie Algebras
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.
15512865
Geometry of the transport equation in multicomponent WKB approximations
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.
15391495
Diagnosing Space Telescope Misalignment and Jitter Using Stellar Images
Accurate knowledge of the telescope's point-spread function (PSF) is essential for the weak gravitational lensing measurements that hold great promise for cosmological constraints. For space telescopes, the PSF may vary with time due to thermal drifts in the telescope structure, and/or due to jitter in the spacecraft pointing (ground-based telescopes have additional sources of variation). We describe and simulate a procedure for using the images of the stars in each exposure to determine the misalignment and jitter parameters, and reconstruct the PSF at any point in that exposure's field of view. As a case study, the simulation uses the design of the Supernova Acceleration Probe (SNAP) telescope. Stellar-image data in a typical exposure determines secondary-mirror positions as precisely as 20 nm. The PSF ellipticities and size, which are the quantities of interest for weak lensing are determined to 4.0 × 10^-4 and 2.2 × 10^-4 accuracies, respectively, in each exposure, sufficient to meet weak-lensing requirements. We show that, for the case of a space telescope, the PSF estimation errors scale inversely with the square root of the total number of photons collected from all the usable stars in the exposure.
123911099
Branching fraction measurements of the decays $B \to eta_c K$, where $eta_c \to K \bar{K} \pi$ and $eta_c \to 4 K$
8083064
Astrophysically triggered searches for gravitational waves: status and prospects
In gravitational-wave detection, special emphasis is put onto searches that focus on cosmic events detected by other types of astrophysical observatories. The astrophysical triggers, e.g. from γ-ray and x-ray satellites, optical telescopes and neutrino observatories, provide a trigger time for analyzing gravitational-wave data coincident with the event. In certain cases the expected frequency range, source energetics, directional and progenitor information are also available. Beyond allowing the recognition of gravitational waveforms with amplitudes closer to the noise floor of the detector, these triggered searches should also lead to rich science results even before the onset of Advanced LIGO. In this paper we provide a broad review of LIGO's astrophysically triggered searches and the sources they target.
118905429
Resonance structure of tau- ---> K- pi+ pi- nu(tau) decays
Using a sample of 4.7/fb integrated luminosity accumulated with the CLEO II detector at the Cornell Electron Storage Ring (CESR), we investigate the mass spectrum and resonant structure in tau->Kpipi decays. We measure the relative fractions of K1(1270) and K1(1400) resonances in these decays, as well as the K1 masses and widths. Our fitted K1 resonances are somewhat broader than previous hadroproduction measurements, and in agreement with recent LEP results from tau decay. The larger central value of our measured width supports models which attribute the small tau->Kpipi branching fraction to larger K1 widths than are presently tabulated. We also determine the Ka-Kb mixing angle theta_K.
114186762
Conceptual design for a silicon tracker at the SSC