16865378
Hochschild cohomology and characteristic classes for star products
We show that the Hochschild cohomology of the algebra obtained by formal deformation quantization on a symplectic manifold is isomorphic to the formal series with coefficients in the de Rham cohomology of the manifold. The cohomology class obtained by differentiating the star-product with respect to the deformation parameter is seen to be closely related to the characteristic class of the quantization. A fundamental role in the analysis is played by ``quantum Liouville operators,'' which rescale the deformation parameter in the same way in which Liouville vector fields scale the Poisson structure (or the units of action). Several examples are given.
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.
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.
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.
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.
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.
117342592
Sensitivity to Gravitational Waves from Compact Binary Coalescences Achieved during LIGO's Fifth and Virgo's First Science Run
We summarize the sensitivity achieved by the LIGO and Virgo gravitational wave detectors for compact binary coalescence (CBC) searches during LIGO's fifth science run and Virgo's first science run. We present noise spectral density curves for each of the four detectors that operated during these science runs which are representative of the typical performance achieved by the detectors for CBC searches. These spectra are intended for release to the public as a summary of detector performance for CBC searches during these science runs.
124064020
Of Symmetries and Factories, Matter and Antimatter
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.
15479152
Measurements of the mass, total width, and two-photon partial width of the eta(c) meson.
Using 13.4 fb(-1) of data collected with the CLEO detector at the Cornell Electron Storage Ring, we have observed 300 events for the two-photon production of ground-state pseudoscalar charmonium in the decay eta(c)-->K(0)(S)K-/+pi(+/-). We have measured the eta(c) mass to be [2980.4+/-2.3 (stat)+/-0.6 (syst)] MeV and its full width as [27.0+/-5.8 (stat)+/-1.4 (syst)] MeV. We have determined the two-photon partial width of the eta(c) meson to be [7.6+/-0.8 (stat)+/-0.4 (syst)+/-2.3 (br)] keV, with the last uncertainty associated with the decay branching fraction.
29052022
The search for millicharged particles at SLAC
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.
126259018
Search for the decay $B^0 \to \gamma \gamma$