Construction of non-Abelian gauge theories on noncommutative spaces

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. Received: 13 June 2001 / Published online: 19 July 2001     

Quasielastic gamma-ray scattering from glycerol

The Mössbauer scattering instrument at the Missouri University Research Reactor (MURR) has been used to study the liquid dynamics of glycerol as a function of temperature. The measurements were made by observing the Mössbauer gamma rays from the 46.5-keV level in¹⁸³W scattered in the direction corresponding to the first liquid structure peak atQ=1.36 Å^–1. The widths of the Mössbauer velocity spectra were found to be quasielastically broadened by 3.1 eV at 24 °C up to 55 eV at 113 °C. The broadening varied quadratically with temperature above the melting point, but showed a linear dependence when plotted versus the absolute temperature divided by the viscosity. As discussed by Singh and Mullen, this latter dependence is expected in the continuous diffusion limit. The original analysis by Singwi and Söjlander was carried out for a diffusing Mössbauer ion, where the observed cross section is the Fourier transform of the self-correlation function. Our case requires the use of the paircorrelation function. Quantitative calculations as well as further experiments are needed.This work was performed with the support of the US Department of Energy under Grant Nos. DE-FG02-85ER45200 and DE-FG02-85ER45199.     

Impact of Substitution Pattern and Chain Length on the Thermotropic Properties of Alkoxy-Substituted Triphenyl-Tristriazolotriazines

Tristriazolotriazines (TTTs) with a threefold alkoxyphenyl substitution were prepared and studied by DSC, polarized optical microscopy (POM) and X-ray scattering. Six pentyloxy chains are sufficient to induce liquid-crystalline behavior in these star-shaped compounds. Thermotropic properties of TTTs with varying substitution patterns and a periphery of linear chains of different lengths, branching in the chain and swallow-tails, are compared. Generally, these disks display broad and stable thermotropic mesophases, with the tangential TTT being superior to the radial isomer. The structure–property relationships of the number of alkyl chains, their position, length and structure were studied.     

External fields as intrinsic geometry

There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external fields which can be absorbed into an appropriate redefinition of the geometry, this time a noncommutative one. We shall also recall some previous incidences of the same phenomena involving bosonic field theories. It is known that some such theories on the commutative geometry of space-time can be re-expressed as abelian-gauge theory in an appropriate noncommutative geometry. The noncommutative structure can be considered as containing extra modes all of whose dynamics are given by the one abelian action. Received: 1 December 2000 / Published online: 23 January 2001     

Surface characterization of functional poly(diacetylene) and poly(butadiene) mono- and multilayers

The surface properties of Langmuir-Blodgett mono- and multilayers of a variety of amphiphilic poly(diacetylene)s and poly(butadiene)s were investigated by contact angle, streaming potential, ellipsometry, and X-ray photoelectron spectroscopic (XPS) measurements. Captive air and octane angles varied between approximately 60° and 105° for hydrophobicx-layers and 31° to 46° for hydrophilic surfaces depending on the particular head group, whereas advancing angles determined via the vertical plate method are considerably higher. Negative streaming potentials were obtained for all surfaces. Positively charged monolayers yielded less negative- potential values (–28 mV) than negatively charged (–52 mV) or hydrophobic (–50 mV) layers. Ellipsometry measurements yielded an average layer thickness of 27±6 Å for 3 to 11 layers. X-ray photoelectron spectroscopy results qualitatively confirmed the expected composition. All of the samples, which were handled and stored in air after deposition and polymerization, were surface oxidized.Dedicated to Prof. Dr. F. H. Müller.