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

The Risk of Reliance on Perceived Risk

Professor Cross\u27s comment is closely related to the debate between Thompson and Valverde. Using examples that do not commonly appear in the Risk literature, he argues that: Giving weight to perceived Risk may seem liberal insofar as it gives more say to the little guy, but giving perceived Risk too much weight could have distinctly illiberal social consequences

Seifert Manifolds

A Seifert manifold is a 3-dimensional manifold with a circle action. It is a circle bundle (with singularities) over a 2-dimensional orbifold. In this note, we discuss a generalized Seifert manifolds. By definition, they have bundle-like structures whose fibers are infra- homogeneous spaces; that is, the fibers are flat manifolds, almost flat manifolds, etc. We prove existence, uniqueness, rigidity theorems. Many interesting properties and applications are presented.Comment: 61 page

Structure of Stationary Photodissociation Fronts

The structure of stationary photodissociation fronts is revisited. H_2 self- shielding is discussed, including the effects of line overlap. We find that line overlap is important for N(H_2) > 10^{20} cm^{-2}. We compute multiline UV pumping models, and compare these with simple analytic approximations for the effects of self-shielding. The overall fluorescent efficiency of the photodissociation front is obtained for different ratios of chi/n_H (where chi characterizes the intensity of the incident UV) and different dust extinction laws. The dust optical depth tau_{pdr} to the point where 50% of the H is molecular is found to be a simple function of a dimensionless quantity phi_0 depending on chi/n_H, the rate coefficient for H_2 formation on grains, and the UV dust opacity. The fluorescent efficiency of the PDR also depends primarily on phi_0 for chi<3000 and n_H<10^4 cm^{-3}; for stronger radiation fields and higher densities radiative and collisional depopulation of vibrationally-excited levels interferes with the radiative cascade. The emission spectrum from the PDR is essentially independent of the color temperature $T_{color}$ of the incident UV for T_{color}>10^4K, but shows some sensitivity to the v-J distribution of newly-formed H_2. The 1-0S(1)/2-1S(1) and 2-1S(1)/6-4Q(1) intensity ratios, the ortho/para ratio, and the rotational temperature in the $v$=1 and $v$=2 levels are computed as functions of the temperature and density, for different values of chi and n_H. We apply our models to the reflection nebula NGC 2023. We are best able to reproduce the observations with models having chi=5000, n_H=10^5 cm^{-3}.Comment: 50 pages, 24 eps figures, uses aaspp4.sty . To appear in Ap.

Light Hadron Spectroscopy on Coarse Lattices with O(a^2) Mean-Field Improved Actions

The masses and dispersions of light hadrons are calculated in lattice QCD using an O(a^2) tadpole-improved gluon action and an O(a^2) tadpole-improved next-nearest-neighbor fermion action originally proposed by Hamber and Wu. Two lattices of constant volume with lattice spacings of approximately 0.40 fm and 0.24 fm are considered. The results reveal some scaling violations at the coarser lattice spacing on the order of 5%. At the finer lattice spacing, the calculated mass ratios reproduce state-of-the-art results using unimproved actions. Good dispersion and rotational invariance up to momenta of pa ~ 1 are also found. The relative merit of alternative choices for improvement operators is assessed through close comparisons with other plaquette-based tadpole-improved actions.Comment: 17 page RevTeX manuscript. 7 Figures. This and related papers may also be obtained from http://www.physics.adelaide.edu.au/~dleinweb/Publications.htm