Symmetries, conservation laws, cohomology of Maxwell's equations in Minkowski space

Abstract:
A survey of recent classification work on symmetries and conservation laws of the free Maxwell field equations is given. The results include: (i) a complete classification of local symmetries and conservation laws to all orders, including novel chiral conserved tensors and chiral symmetry operators; (ii) new classes of geometric nonlocal symmetries and conservation laws obtained using self-dual potentials; (iii) locality formulas for symmetries and conservation laws of potential
systems, derived through cohomology theorems for Maxwell's equations.

Generalizations of this work to free spin $s$ field equations also will be outlined.