# On Lagrangian and non-Lagrangian conformal-invariant nonlinear electrodynamics

## TL;DR

This paper develops a general framework for nonlinear conformal-invariant electrodynamics, introducing constitutive equations dependent on conformal invariants, and derives formulas for possible Lagrangian densities extending classical electrodynamics.

## Contribution

It presents a unified approach to describe both Lagrangian and non-Lagrangian nonlinear conformal electrodynamics using conformal-invariant functionals.

## Key findings

- Derived a general formula for Lagrangian densities in conformal-invariant nonlinear electrodynamics.
- Characterized constitutive equations dependent on conformal invariants.
- Extended classical electrodynamics to include nonlinear, conformally invariant theories.

## Abstract

A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on conformal-invariant functionals of the field strengths. This allows a characterization of Lagrangian and non-Lagrangian theories. We obtain a general formula for possible Lagrangian densities in nonlinear conformal-invariant electrodynamics. This generalizes the standard Lagrangian of classical linear electrodynamics so as to preserve the conformal symmetry.