Abstract
It is shown that—in analogy to what has been recently suggested for a quantum n‐level system—in a multimode analysis of the free electron laser (FEL) Hamiltonian picture, one can use the (n2−1)‐dimensional vector F↘ of SU(n) to describe the main FEL dynamics. The FEL coherence properties are discussed by this group‐theoretical approach, and a critical analysis of related Casimir invariants and conservation laws is given.