Electromagnetic Deflection of Spinning Particles

We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a manifestly covariant Lagrangian, if the classical degrees of freedom are appropriately chosen. It is shown that the equations obtained encompass the well-tested Lorentz force and Thomas--Bargmann--Michel--Telegdi spin equations, as well as providing a definite specification of the classical _magnetic_dipole_ force_, whose exact form has been the subject of recent debate. Radiation reaction---the force and torque on an accelerated particle due to its self-interaction---is neglected at this stage.Comment: 18 pp. (latex, uses revtex 3), UM-P-92/9

The Foldy-Wouthuysen transformation

The Foldy-Wouthuysen transformation of the Dirac Hamiltonian is generally taught as simply a mathematical trick that allows one to obtain a two-component theory in the low-energy limit. It is not often emphasized that the transformed representation is the only one in which one can take a meaningful *classical limit*, in terms of particles and antiparticles. We briefly review the history and physics of this transformation.Comment: Standard LaTeX, 6 page

Geografia e a cartografia escolar no ensino básico: uma relação complexa – percursos e possibilidades

Esta pesquisa tem o intuito de diagnosticar possíveis deficiências dos alunos em relação à alfabetização cartográfica. Traz um olhar da construção do conhecimento escolar, através das contribuições da Epistemologia Genética e da Epistemologia da Complexidade. Discute o trabalho interdisciplinar entre a Geografia e a Cartografia. Tem como objetivo principal: estudar a construção do conhecimento cartográfico e as suas implicações na educação básica do componente curricular Geografia a partir das práticas existentes em escolas da rede pública e privada. É uma pesquisa qualitativa e apoia-se no Paradigma da Complexidade. Foram realizadas oficinas enquanto atividades investigativas

The Thomas rotation

We review why the Thomas rotation is a crucial facet of special relativity, that is just as fundamental, and just as "unintuitive" and "paradoxical", as such traditional effects as length contraction, time dilation, and the ambiguity of simultaneity. We show how this phenomenon can be quite naturally introduced and investigated in the context of a typical introductory course on special relativity, in a way that is appropriate for, and completely accessible to, undergraduate students. We also demonstrate, in a more advanced section aimed at the graduate student studying the Dirac equation and relativistic quantum field theory, that careful consideration of the Thomas rotation will become vital as modern experiments in particle physics continue to move from unpolarized to polarized cross-sections.Comment: 20 pages, plain LaTeX, no figures, no macros, no style sheet