Laser-driven Particle Mechanics via Celestial Mechanics

Compared to laser-driven particle mechanics, celestial mechanics is a highly developed science. Progress in the former could be speeded up considerably if the questions that have been asked, the mathematical techniques that have been developed, and the principles that have been formulated could be extended from the latter to the former.

It is a well-known fact that the Kepler problem of, say, a planet orbiting around a star (``two-body problem'') plays a role of key importance in celestial mechanics. This importance extends to the problem of a charge in the e.m. field of a travelling plane wave in laser-driven particle mechanics in the following three respects:

• Both problems are exactly soluble, i.e. are integrable dynamical systems.
• Both problems have their repective laws: (i) Kepler's second law (equal areas swept out in equal times), and (ii) equal phases (educed from Eqs.(31)-(32) elapse in equal proper times. The corresponding conserved quantities are (i) the angular momentum and (ii) the momentum $P_v=P_t+P_z$, as one can see from Eq.(24).
• By having the planet orbit around a double star system Kepler's problem becomes an in-general nonintegrable dynamical system.

  !!!!! parallelism to be completed