Infinite Sequence of Poincare Group Extensions: Structure and Dynamics

Understand

We study the structure and dynamics of the infinite sequence of extensions of the Poincar{\'e} algebra whose method of construction was described in a previous paper [1].

• We give explicitly the Maurer-Cartan (MC) 1-forms of the extended Lie algebras up to level three.
• Using these forms and introducing a corresponding set of new dynamical couplings, we construct an invariant Lagrangian, which describes the dynamics of a distribution of charged particles in an external electromagnetic field.
• At each extension, the distribution is approximated by a set of moments about the world line of its center of mass and the field by its Taylor series expansion about the same line.