# Conformal invariance of Electromagnetic field action

What is the significance of Conformal invariance of Electromagnetic field action? What does it lead to? And how can we break it?

## 1 Answer

Maxwell action is conformally invariant basically because of masslessness of photon, which implies that the action doesn't contain any dimensionful parameters. Such parameters would set the scale, and thus break the scaling symmetry. There is no proof that in $4D$ the scale invariance implies full conformal symmetry, but there are no counterexamples known. So the easiest way to break the conformal symmetry is to add the mass term to the Lagrangian $-m^2 A^{\mu} A_{\mu}$.

Conformal invariance allows us to obtain many new solutions to the equations of motion from the given one -- any solution obtained by acting the symmetry generator on the solution is again a solution.

• Just to add to the answer: one technical consequence of conformal invariance is that, classically at least, the trace of the energy-momentum tensor vanishes. – Gabriel Cozzella Mar 10 '18 at 12:19