|XXXII Workshop on Geometric Methods in Physics||30.06-6.07.2013|
Participants of Workshop
Participants of School
Nonlineear conformal-invariant electrodynamics in (4+2)-dimensional spacetime
The conformal compactification of (3+1)-dimensional Minkowski spacetime, as is well-known, can be identified with the projective light cone in (4+2)-dimensional spacetime. In this space the conformal group acts linearly via rotations, and fields satisfying conformal-invariant linear
Maxwell equations can be defined. Here we consider nonlinear, conformal-invariant equations for the higher-dimensional Maxwell fields. Nonlinear constitutive equations are expressed in terms of a pair of invariant functionals. We write their transformation properties under conformal inversion in some different coordinate systems. We then explore them in relation to the class of nonlinear constitutive equations for classical electromagnetism in 3+1 dimensions respecting conformal symmetry (including Lagrangian and non-Lagrangian systems). The talk is based on continuing joint work by the presenter with Steven Duplij (Kharkov National University, Ukraine) and Vladimir Shtelen (Rutgers University, USA).
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