Exterior Differential Systems for Yang-Mills Theories

Exterior differential systems are given, and their Cartan characters calculated, for Maxwell and SU(2)-Yang-Mills equations in dimensions from three to six.Comment: This is a contribution to the Special Issue "Elie Cartan and Differential Geometry", published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGM

Specialized Orthonormal Frames and Embedding

We discuss some specializations of the frames of flat orthonormal frame bundles over geometries of indefinite signature, and the resulting symmetries of families of embedded Riemannian or pseudo-Riemannian geometries. The specializations are closed sets of linear constraints on the connection 1-forms of the framing. The embeddings can be isometric, as in minimal surfaces or Regge-Teitelboim gravity, or torsion-free, as in Einstein vacuum gravity. Involutive exterior differential systems are given, and their Cartan character tables calculated to express the well-posedness of the underlying partial differential embedding and specialization equations

An experimental determination of the absolute oscillator strengths of some resonance transitions of chromium and nickel

A brief account is given of the classical electron theory of anomalous dispersion and line absorption. The oscillator strength, or f-value, is introduced as the factor involved in taking over the results of classical theory in a modern quantum mechanical formulation. The relation between f-values and the transition probabilities of Einstein is derived. A summary of methods for experimental determination of f-values for atomic transitions is given, and in particular the method of total absorption is considered in detail. The equivalent width or total absorption of an absorption line is defined, and the relation of this to the oscillator strength of the line, the so-called curve of growth, qualitatively explained. The laboratory apparatus used in the present investigation is described in detail, as are the methods of obtaining and reducing the experimental data. An account is given of unsuccessful experiments on the resonance lines of Ca. Absolute nf-values obtained for three lines of Cr are reported, and on the basis of unsatisfactory vapor pressure data, tentative absolute f-values for these lines are assigned. Absolute f-values for three lines of the Ni spectrum are reported, the vapor pressure data for Ni being reliable. A conversion factor is obtained by which the relative gf-values for Ni given by King may be reduced to an absolute scale.</p

Interview with Frank B. Estabrook

An interview on February 28, 2007, with Frank B. Estabrook, Distinguished Visiting Scientist at the Jet Propulsion Laboratory. Dr. Estabrook received his MS (1947) and his PhD (1950) in spectroscopy at Caltech. He joined JPL in 1960, becoming senior resarch scientist there from 1979 to 2006 and Distinguished Visiting Scientist in 2006. In this interview, he discusses his youthful fascination with general relativity and his later research, with H. D. Wahlquist, J. W. Armstrong, and B. Bertotti, on the development of proposals to detect gravity waves by means of the Doppler tracking of spacecraft. He discusses the involvement of Caltech theoretical physics professor K. S. Thorne in these efforts, and the inclusion of gravity-wave experiments in the Galileo, Mars Observer, Ulysses, and Cassini missions

Data Combinations Accounting for LISA Spacecraft Motion

LISA is an array of three spacecraft in an approximately equilateral triangle configuration which will be used as a low-frequency gravitational wave detector. We present here new generalizations of the Michelson- and Sagnac-type time-delay interferometry data combinations. These combinations cancel laser phase noise in the presence of different up and down propagation delays in each arm of the array, and slowly varying systematic motion of the spacecraft. The gravitational wave sensitivities of these generalized combinations are the same as previously computed for the stationary cases, although the combinations are now more complicated. We introduce a diagrammatic representation to illustrate that these combinations are actually synthesized equal-arm interferometers.Comment: 10 pages, 3 figure