The Dynamics of Compact Laser Pulses

We discuss the use of a class of exact finite energy solutions to the vacuum source-free Maxwell equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged point particles. These compact solutions are classified in terms of their chiral content and their influence on particular charge configurations in space. The results of such classical interactions motivate a phenomenological quantum description of a propagating laser pulse in a medium in terms of an effective quantum Hamiltonian.