**Ulrich H. Gerlach**

The dynamics of laser-driven charged
particles is developed telegraphically from four different
perspectives, all of them relativistic: Lagrangian, Hamiltonian,
Hamilton-Jacobi, and action-angle. Their unifying idea is the principle
of constructive interference. Its physical and mathematical appeal
arises from its conceptual unit economy and simplicity.

Being driven by a travelling plane wave, the dynamics of a charged particle is that of an integrable exactly soluble dynamical system having four degrees of freedom. Each one is a uniform rotation whose frequency depends on the action of the that degree, and whose motion is related to the physical motion by the principle of constructive degree of freedom.

- Contents
- Motivational Overview
- Lagrangian and Hamiltonian Formulation of Mechanics.
- Advantage of the Hamiltonian Formulation.
- The Dynamical Phase
- The Hamilton-Jacobi Equation for a Relativistic Particle.
- Solution to the Hamilton-Jacobi Equation
- Dynamical Phase as Physical
- The Principle of Constructive Interference
- Laser-driven Particle Mechanics via Celestial Mechanics
- Phase Flow: Its Trajectories and Transformations
- Action-Angle Representation

- Conclusion
- About this document ...

Ulrich Gerlach 2005-11-07