Vector potentials in gauge theories in flat spacetime

A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under 4D frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential $A$ always transforms homogeneously under 4D rotations in spacetime, but if the gauge is changed by the rotation, one can restore the gauge back to the original gauge by adding an inhomogeneous term. It is then "not a 4-vector", but two: one for rotation and one for translation. For such a gauge, it is much more important to preserve {\it explicit} homogeneous Lorentz covariance by simply skipping the troublesome gauge-restoration step. A gauge-independent separation of $A$ into a dynamical term and a non-dynamical term in Abelian gauge theories is re-defined more generally as the terms caused by the presence and absence respectively of the 4-current term in the inhomogeneous Maxwell equations for $A$. Such a separation {\it cannot} in general be extended to non-Abelian theories where $A$ satisfies nonlinear differential equations. However, in the linearized iterative solution that is perturbation theory, the usual Abelian quantizations in the usual gauges can be used. Some nonlinear complications are briefly reviewed.Comment: 7 page

Meson-Meson Scattering in Relativistic Constraint Dynamics

Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. We use this formalism to describe a microscopic theory of meson-meson scattering as a relativistic generalization of the nonrelativistic quark-interchange model developed by Barnes and Swanson.Comment: 5 pages, 1 figure in LaTex, talk present at the First Meeting of the APS Topical Group on Hadronic Physics (Fermilab, October 24-26, 2004