Half-whole Dimensions in Quaternionic Quantum Mechanics

We introduce {\em half-whole} dimensions for quaternionic matrices and propose a quaternionic version of the Frobenius-Schur theorem which allows us to obtain the proper quaternionic dimensionality for the representations of the Dirac and Duffin-Kemmer-Petiau (DKP) algebras.Comment: 9 pages, Revtex, Prog. Theor. Phys. (to be published

Quaternions and Special Relativity

We reformulate Special Relativity by a quaternionic algebra on reals. Using {\em real linear quaternions}, we show that previous difficulties, concerning the appropriate transformations on the $3+1$ space-time, may be overcome. This implies that a complexified quaternionic version of Special Relativity is a choice and not a necessity.Comment: 17 pages, latex, no figure

Localized Beams and Dielectric Barriers

Recalling the similarities between the Maxwell equations for a transverse electric wave in a stratified medium and the quantum mechanical Schroedinger equation in a piece-wise potential, we investigate the analog of the so called particle limit in quantum mechanics. It is shown that in this limit the resonance phenomena are lost since individual reflection and transmission terms no longer overlap. The result is a stationary zebra-like response with the intensity in each stripe calculable.Comment: 8 pages, 3 figure

Laser Interaction with a Dielectric Block

Some optical experiments provide the easiest way to test quantum mechanical predictions. Such a situation applies to a laser beam traversing a dielectric structure. The dielectric structure mir- roring quantum mechanical potentials. The simplest of these, studied in this paper, involves a single dielectric block. We exhibit both by analytic and numerical calculations explicit examples of total coherence and total incoherence phenomena. Which case appears depends upon the angle of incidence of the laser beam and/or the dimensions of beam vs block width. Unlike our previ- ous studies our calculations here are three-dimensional, although, with suitable approximations, somewhat simpler planar expressions can be derived.Comment: 14 pages, 3 figure