Lester L. DeRaad

Casimir effect in dielectrics

We reconsider the Casimir (van der Waals) forces between dielectrics with plane, parallel surfaces for arbitrary temperature, using the methods of source theory. The general results of Lifshitz are confirmed, and are shown to imply the correct forces on metal surfaces. The same phenomena give rise to contributions to the surface tension and the latent heat of an idealized liquid, contributions which, unfortunately, are not well defined since they depend upon a momentum cutoff. However, with a reasonable value for this cutoff, qualitative agreement with the experimentally observed surface tension and latent heat of liquid helium at absolute zero is obtained.

Casimir self-stress on a perfectly conducting spherical shell☆

Abstract The Casimir stress on a perfectly conducting uncharged sphere, due to occurrence of fluctuations in the electromagnetic field, is calculated using a source theory formulation. Two independent methods are employed: we compute (1) the total Casimir energy inside and outside the sphere, and (2) the radial component of the stress tensor on the surface. It is necessary to exercise care in allowing the field points to overlap; a correct limiting procedure supplies a “cutoff” in the frequency integration. In spite of numerous technical improvements, the result of Boyer, that the self-stress is repulsive (and not attractive as Casimir hoped), is confirmed unambiguously. The magnitude of the Casimir energy of a sphere of radius a is found, by numerical and analytic techniques, to be E = ( h c 2a )(0.09235) , also in agreement with the very recent result of Balian and Duplantier.

Casimir self-stress on a perfectly conducting cylindrical shell

Abstract We compute the Casimir stress on a perfectly conducting cylindrical shell, due to quantum field fluctuations (zero-point energy) in both the interior and exterior regions, using a Greens dyadic formulation for the field strengths. To obtain a finite answer, a frequency cutoff must be inserted, but the result is independent of that cutoff. The Casimir stress is found to be attractive, the Casimir energy per unit length for a cylinder of radius a being E = −0.014 a 2 .

Nonrelativistic Dyon-Dyon Scattering

Abstract The nonrelativistic problem of the scattering of two dyons (including the case of electron scattering by magnetic monopoles) is systematically studied, both classically and quantum mechanically, with a view toward the discrimination between various combinations of electric and magnetic charges. We analyze the classical cross section with particular attention to the interesting phenomena which occur for large angle scattering, the “rainbows” and “glory,” where the cross section becomes infinite. Quantum mechanically, we find that these infinities do not occur and that, when the partial wave scattering amplitude is summed, a very elaborate structure emerges for the cross section, which depends sensitively upon the electric and magnetic charges of the particles, as well as on their relative speed. We further discuss a large modification, leading to spin flip and nonflip amplitudes, due to the dipole moments of the particles. Numerical results are presented for a variety of values of these parameters. In principle, these results could be used to distinguish the δ-ray distributions produced by the various species of electrically and magnetically charged particles. Quite apart from the experimental implications of our numerical results, we have made a number of theoretical improvements and extensions. Numbered among these are the consideration of dyons and particles having dipole moments, and the explicit demonstration, based on the methods of angular momentum, that the differential cross section is independent of the choice of singularity line.

Two muon events and new particle production

Abstract Schwingers interpretation of the narrow resonances coupling to the electric current suggests that there are charged vector particles that decay weakly, having mass of perhaps 3.4 GeV. These may have already been seen in neutrino scattering experiments.

Anomalous spectral regions in source theory

We generate a double spectral representation for a scattering process akin to Compton scattering, with particular emphasis on virtual forward scattering. For particular choices of particle masses and momentum transfers, the spectral region ranges over negative mass-squared values. These results are shown to be consistent with single spectral representations for the same processes. Our results coincide with those of Fronsdal, Norton, and Mahanthappa, but are arrived at in a more direct manner.

Strings and gauge invariance

Within the context of the nonrelativistic theory of dyons, we study a number of interrelated issues concerning the quantum formulation of magnetic charge. We begin by solving the two‐body Schrodinger equation for an arbitrarily oriented singularity line (string) in terms of the known solutions with the string on the z axis. Charge quantization conditions emerge by requiring that the wavefunctions be single valued. The general solutions express the necessary gauge covariance of the wavefunctions. These results provide a basis for the reconsideration of the phase factor in the dyon–dyon scattering amplitude. Finally, the connection between the formulations in terms of vector potentials and in terms of intrinsic spin is investigated. This approach leads to a rederivation of the gauge transformation properties of the theory.

Weak-Boson Triangle Anomalies

The causal methods of source theory are used to calculate the triangle anomalies of weak bosons (W plus or minus and Z) in a unified gauge theory of weak and electromagnetic interactions (not involving heavy leptons). The pseudoelectric form factors for these particles are also presented.