Classical particles with internal structure: general formalism and application to first-order internal spaces

Abstract

Group theoretic methods are used to systematically classify all possible internal structures for an elementary classical relativistic particle in terms of coset spaces of SL(2,C) with respect to its continuous subgroups. The allowed internal spaces Q are separated into first- and second-order ones, depending on whether a canonical description can be given using Q itself or if it needs the cotangent bundle T^∗Q. Three of the former are found, one corresponding to the use of a Majorana spinor as the internal variable, the other two related to orbits in the Lie algebra of SO(3,1) under the adjoint action. For the latter two, a Lagrangian description of an elementary object with the corresponding internal space is set up, and the dynamics studied.