Hamiltonian Picture of the Free Electron Laser and Unitary Symmetries

摘要

It is shown that the invariance of the free electron laser (FEL) quantum Hamiltonian in a multimode picture can be used to describe the FEL dynamics in terms of an (nsq-l)-dimensional vector F, built up by SU(n) generators. The equation of motion for F amounts to a rotation in SU(n) space plus a dephasing term (due to the noncommutativity of the electron variables). The result that coherence is not preserved under quantum FEL operation is recovered without explicit solutions. Coherence is regained in the classical and in the semiclassical limit. The constants of motion (apart from the total momentum conservation) are given by the Casimir operators of U(n).