Nonlocal symmetries are obtained for Maxwell's equations in three space–time dimensions
through the use of two potential systems involving scalar and vector potentials for the
electromagnetic field. Corresponding nonlocal conservation laws are derived from these
symmetries. The conservation laws yield nine functionally independent constants of motion
which cannot be expressed in terms of the constants of motion arising from local
conservation laws for space–time symmetries. These nine constants of motion represent …

We derive new nonlocal symmetries and corresponding new nonlocal conservation laws for
the free-space Maxwell's equations (ME) in 3+ 1 space-time dimensions. These results arise
from a detailed point symmetry analysis of several potential systems associated with ME:(1)
LPS: the standard Lagrangian potential system,(2) A-LPS: LPS augmented by the Lorentz
gauge,(3) PS: a natural non-Lagrangian potential system with dual vector potentials, and (4)
A-PS: PS augmented by dual Lorentz gauges. The well-known (local) space-time …