Covariant electromagnetic projection operators and a covariant description of charged particle guiding centre motion

Abstract

For non-null electromagnetic fields, a pair of covariant field projection operators is obtained which separate four-space into mutually orthogonal two-flats spanned by the field eigenvectors associated, respectively, with real or imaginary eigenvalues. In appropriate limits, these projections generalise the notion of components perpendicular to and parallel with a particular E or B direction. These operators are used in a relativistic covariant analysis of the motion of a charged particle subject to a constant electromagnetic field. The covariant projections of the motion are uncoupled and separate orbit equations for each projection are presented. This analysis is related to a generalisation of the guiding centre concept. A covariant guiding centre treatment is developed and applied to the situation where slowly changing field inhomogeneities exist.