Stability for a class of bilocal Hamiltonians

We introduce a method to establish stability of non-local interactions, and we apply this method to certain polynomial non-linear field theory. The non-local potential must satisfy the property ofslow decrease at infinity in Fourier space (SDI).Dedicated to Huzihiro ArakiSupported in part by the National Science Foundation under Grant PHY91-20626     

An Exchange Identity for Non-linear Fields

We establish a useful identity for intertwining a creation or annihilation operator with the heat kernel of a self-interacting bosonic field theory.     

Green's functions for Maxwell's equations: application to spontaneous emission

We present a new formalism for calculating the Green's function for Maxwell's equations. As our aim is to apply our formalism to light scattering at surfaces of arbitrary materials, we derive the Green's function in a surface representation. The only requirement on the material is that it should have periodicity parallel to the surface. We calculate this Green's function for light of a specific frequency and a specific incident direction and distance with respect to the surface. The material properties entering the Green's function are the reflection coefficients for plane waves at the surface. Using the close relationship between the Green's function and the density of states (DOS), we apply our method to calculate the spontaneous emission rate as a function of the distance to a material surface. The spontaneous emission rate can be calculated using Fermi's Golden Rule, which can be expressed in terms of the DOS of the optical modes available to the emitted photon. We present calculations for a finite slab of cylindrical rods, embedded in air on a square lattice. It is shown that the enhancement or suppression of spontaneous emission strongly depends on the frequency of the light. This revised version was published online in November 2006 with corrections to the Cover Date.     

The two-dimensional,N=2 Wess-Zumino model on a cylinder

We construct a family of supersymmetric, two-dimensional quantum field models. We establish the existence of the HamiltonianH and the superchargeQ as self-adjoint operators. We establish the ultraviolet finiteness of the model, independent of perturbation theory. We develop functional integral representations of the heat kernel which are useful for proving estimates in these models. In a companion paper [1] we establish an index theorem forQ, an infinite dimensional Dirac operator on loop space. This paper and, another related one [2], provide the technical justification for our claim thatQ is Fredholm, and for our computation of its index by a homotopy onto quantum mechanics.Supported in part by the National Science Foundation under Grant DMS/PHY 86-45122Hertz Foundation Graduate Fellow     

Les polyélectrolytes à l'interface liquide–liquide

The behavior of films of polyelectrolytes at the water-organic liquid interface depends on the nature of the interface and the pH of the substratum. The present paper investigates the influence of these two factors on the cohesive forces between monomer units. Two polyelectrolytes were studied: poly(methacrylic acid) (APM) and poly-2-vinylpyridine (2-PVP). In the case of uncharged films, the collapse pressure decreases when the polarity of the organic phase becomes more important, whereas the term ω/kT, which appears in the theory of Motomura and Matuura, increases. A quantitative relation between the parameter ω/kT and the collapse pressure may be deduced. The behavior of the ionized surface film at different pH values is modified by the choice of the interface. However, there exists a competition between two phenomena: the dissolution of ionized residues in the substratum and the electrostatic repulsion between charges in the surface plane. Depending upon whether the first or the second parameter is more important, we observed that the surface pressure decreased or increased with the degree of ionization.     

The mass gap for Higgs models on a unit lattice

An isomorphism is established between eertain compact and noncompact formulations of Abelian gauge theory on a lattice. For weak coupling, the mass gap predicted by the Higgs mechanism is then established.     

Near-infrared trace-gas sensors based on room-temperature diode lasers

2 monitor designed for field applications using room-temperature diode lasers are presented. Near-infrared DFB lasers operating at 1.57 μm and around 2.0 μm have been used for CO₂ measurements. At ambient concentration levels a resolution of more than two orders of magnitude has been demonstrated at 1.57 μm, at 2 μm the precision is in the order of 0.1 ppm CO₂, and for trace analysis a detection limit of 10 ppb has been obtained. The measurements demonstrate the capability of near-infrared DFB diode lasers for the precise determination of CO₂ concentrations as required for climatological, medical, or industrial applications. Received: 24 February 1998/Revised version: 27 April 1998     

Radical pairs from photolysis of phenoxy dimers

Ultraviolet photolysis of solid samples of the dimers of phenoxy radicals has been found to produce closely associated radical pairs in some cases. An electron spin resonance investigation of these trapped radical pairs is reported in this note.     

Iron pentacarbonyl mediated coupling of benzyl halides to ketones under mild phase transfer conditions.

In a two-phase system (saturated aqueous calcium hydroxide, tetrabutylamnonium sulfate, dichloromethane, iron pentacarbonyl) benzyl bromides are readily carbonylated to dibenzyl ketones; α-α′ dibromoorthoxylene yields the o-quinodimethane iron tricarbonyl complex 8. It is inferred that the reactions proceed through transient generation of the tetracarbonyl ferrate dianion.