115175355
GROUPOID SYMMETRY AND CONSTRAINTS IN GENERAL RELATIVITY
When the vacuum Einstein equations are cast in the form of Hamiltonian evolution equations, the initial data lie in the cotangent bundle of the manifold of Riemannian metrics on a Cauchy hypersurface Σ. As in every Lagrangian field theory with symmetries, the initial data must satisfy constraints. But, unlike those of gauge theories, the constraints of general relativity do not arise as momenta of any Hamiltonian group action. In this paper, we show that the bracket relations among the constraints of general relativity are identical to the bracket relations in the Lie algebroid of a groupoid consisting of diffeomorphisms between space-like hypersurfaces in spacetimes. A direct connection is still missing between the constraints themselves, whose definition is closely related to the Einstein equations, and our groupoid, in which the Einstein equations play no role at all. We discuss some of the difficulties involved in making such a connection. In an appendix, we develop some aspects of diffeology, the basic framework for our treatment of function spaces.
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.
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.
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.
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.
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.
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.
117893040
Seeing the Nature of the Accelerating Physics: It's a SNAP
For true insight into the nature of dark energy, measurements of the precision and accuracy of the Supernova/Acceleration Probe (SNAP) are required. Precursor or scaled-down experiments are unavoidably limited, even for distinguishing the cosmological constant. They can pave the way for, but should not delay, SNAP by developing calibration, refinement, and systematics control (and they will also provide important, exciting astrophysics).
122930718
Measurements of the meson-photon transition form factors of light pseudoscalar mesons at large momentum transfer
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.
11987687
Search for gravitational waves associated with the gamma ray burst GRB030329 using the LIGO detectors
We have performed a search for bursts of gravitational waves associated with the very bright gamma ray burst GRB030329, using the two detectors at the LIGO Hanford Observatory. Our search covered the most sensitive frequency range of the LIGO detectors (approximately 80–-2048   Hz), and we specifically targeted signals shorter than ≃150  ms. Our search algorithm looks for excess correlated power between the two interferometers and thus makes minimal assumptions about the gravitational waveform. We observed no candidates with gravitational-wave signal strength larger than a predetermined threshold. We report frequency-dependent upper limits on the strength of the gravitational waves associated with GRB030329. Near the most sensitive frequency region, around ≃250  Hz, our root-sum-square (RSS) gravitational-wave strain sensitivity for optimally polarized bursts was better than hRSS≃6×10-21  Hz-1/2. Our result is comparable to the best published results searching for association between gravitational waves and gamma ray bursts.
122011694
First upper limits from LIGO on gravitational wave bursts
We report on a search for gravitational wave bursts using data from the first science run of the Laser Interferometer Gravitational Wave Observatory (LIGO) detectors. Our search focuses on bursts with durations ranging from 4 to 100 ms, and with significant power in the LIGO sensitivity band of 150 to 3000 Hz. We bound the rate for such detected bursts at less than 1.6 events per day at a 90% confidence level. This result is interpreted in terms of the detection efficiency for ad hoc waveforms (Gaussians and sine Gaussians) as a function of their root-sum-square strain h(rss); typical sensitivities lie in the range h(rss) ~10^(-19)-10^(-17) strain/√Hz, depending on the waveform. We discuss improvements in the search method that will be applied to future science data from LIGO and other gravitational wave detectors.