Nonlinear approach to electrodynamics

A nonlinear approach to electrodynamics is reviewed. On imposing a nonlinear constraintA A = – ², together with the usual gauge-invariant electromagnetic field Lagrangian, it is found that the resulting equations of motion have, besides the photon, a static spherically symmetric extended solution which may be regarded as a charged particle. A magnetic dipole moment (spin) can also arise as a solution of the equations of motion if, as expected, it is treated as a first-order quantum effect. In the limit for small quantum fields and pointlike charged particles, the quantum mechanical equivalence of the approach with the usual Lagrangian formulation of the electromagnetic interaction of a charged scalar field is heuristically shown. Moreover the possibility of constructing charged fermion fields from the solution having both a charge and a magnetic moment is illustrated. In such an approach the photon is associated with the spontaneous breaking of Lorentz symmetry, and the emission of soft photons does not exhibit any infrared divergences.