# Conformal symmetry transformations and nonlinear Maxwell equations

## TL;DR

This paper explores conformal symmetry in nonlinear Maxwell equations using conformal compactification of Minkowski spacetime, introducing conformal-invariant functionals for nonlinear constitutive relations.

## Contribution

It introduces conformal-invariant functionals of Maxwell fields in a doubled compactified spacetime, advancing the understanding of nonlinear Maxwell theories with conformal symmetry.

## Key findings

- Defined two conformal-invariant functionals of Maxwell fields.
- Established a framework for nonlinear constitutive equations respecting conformal symmetry.
- Discussed potential generalizations from linear to nonlinear theories.

## 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.