Unnatural Acts: Unphysical Consequences of Imposing Boundary Conditions on Quantum Fields

I examine the effect of trying to impose a Dirichlet boundary condition on a scalar field by coupling it to a static background. The zero point -- or Casimir -- energy of the field diverges in the limit that the background forces the field to vanish. This divergence cannot be absorbed into a renormalization of the parameters of the theory. As a result, the Casimir energy of a surface on which a Dirichlet boundary condition is imposed, and other quantities like the surface tension, which are obtained by deforming the surface, depend on the physical cutoffs that characterize the coupling between the field and the matter on the surface. In contrast, the energy density away from the surface and forces between rigid surfaces are finite and independent of these complicationsComment: 10 pages, 3 figures, uses aipproc.cls which is included in upload. allnew.eps replaces figures all.eps and section.ep

Color, Spin, and Flavor-Dependent Forces in Quantum Chromodynamics

A simple generalization of the Breit Interaction explains many qualitative features of the spectrum of hadrons.Comment: 20 pp., 8 EPS figures, LaTeX2e using BoxedEPS, ws-p8-50x6-00.cls macros; contribution to forthcoming published lectures of the Gregory Breit Centennial Symposium, October 1999; email to [email protected]

Comment on the relation between the nonadiabatic coupling and the complex intersection of potential energy curves

Simple relations are discussed that provide a correspondence between the complex intersection of two potential surfaces and the nonadiabatic coupling matrix element between those surfaces. These are key quantities in semiclassical and quantum mechanical theories of collision induced electronic transitions. Within the two state approximation, the complex intersection is shown to be directly related to the location and magnitude of the peak in the nonadiabatic coupling. Two cases are considered: the avoided crossing between two potential surfaces; and the spin orbit interaction due to a P-2 halogen atom. Comparisons are made between the results of the two-state model and the results of ab initio quantum chemical calculations