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Center for Nonlinear Studies |
We begin with Maxwell’s equations for E, B, D, and H. One way to generalize classical electrodynamics is to introduce nonlinear constitutive equations relating the pair (E,B) to the pair (D,H), consistent with the Lorentz symmetry. While the usual, linear equations are incompatible with a Galilean limit obtained by taking the light speed c to infinity, there are interesting nonlinear variations that allow this limit. The method generalizes to Yang-Mills equations, and to supersymmetric theories (and may even have application to the theory of tensionless strings). After developing this idea, I shall describe – in a self-contained way – some current exploration of nonlinear electromagnetism respecting conformal symmetry. Here one writes nonlinear constitutive equations on projective (4+2)-dimensional space-time, where the generators of the conformal group act as rotations, and in which the conformal compactification of (3+1)-dimensional Minkowski space is embedded. The talk is based on joint work with Vladimir Shtelen and Steven Duplij.
Host: Cristiano Nisoli, T-4, CNLS, cristiano@lanl.gov