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arXiv · 1704.00146

Conformal symmetry transformations and nonlinear Maxwell equations

Gerald A. Goldin·Vladimir M. Shtelen·Steven Duplij
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Abstract

We make use of the conformal compactification of Minkowski spacetime $M^{\#}$ to explore a way of describing general, nonlinear Maxwell fields with conformal symmetry. We distinguish the inverse Minkowski spacetime $[M^{\#}]^{-1}$ obtained via conformal inversion, so as to discuss a doubled compactified spacetime on which Maxwell fields may be defined. Identifying $M^{\#}$ with the projective light cone in $(4+2)$-dimensional spacetime, we write two independent conformal-invariant functionals of the $6$-dimensional Maxwellian field strength tensors -- one bilinear, the other trilinear in the field strengths -- which are to enter general nonlinear constitutive equations. We also make some remarks regarding the dimensional reduction procedure as we consider its generalization from linear to general nonlinear theories.

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Gerald A. Goldin, Vladimir M. Shtelen, Steven Duplij. 2017-04-01. Conformal symmetry transformations and nonlinear Maxwell equations. https://arxiv.org/abs/1704.00146

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