Fractional Electromagnetism in Quantum Matter and High-Energy Physics

Understand

We present here a theory of fractional electro-magnetism which is capable of describing phenomenon as disparate as the non-locality of the Pippard kernel in superconductivity and anomalous dimensions for conserved currents in holographic dilatonic models.

• The starting point for our analysis is the observation that the standard current conservation equations remain unchanged if any differential operator that commutes with the total exterior derivative multiplies the current.
• Such an operator, effectively changing the dimension of the current, increases the allowable gauge transformations in electromagnetism and is at the heart of N\"other's second theorem.
• Here we develop a consistent theory of electromagnetism that exploits this hidden redundancy in which the standard gauge symmetry in electromagnetism is modified by the rotationally invariant operator, the fractional Laplacian.