On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics

Recent experimental results such as those on slow light heighten interest i n nonlinear Maxwell theories. We obtain Galilei covariant equations for ele ctromagnetism by allowing special nonlinearities in the constitutive equati ons only, keeping Maxwell's equations unchanged. Combining these with linea r or nonlinear Schrodinger equations, e.g., as proposed by Doebner and Gold in, yields a consistent, nonlinear, Galilean Schrodinger-Maxwell electrodyn amics. (C) 2001 Elsevier Science B.V. All rights reserved.