Helicity and the Electromagnetic Field

The structure of the Poincaré group gives, under all conditions, an equation of field helicity which reduces to the Maxwell equations and also gives cyclic relations between field components. If the underlying symmetry of special relativity is represented by the Poincaré group, it follows that the Maxwell equations and the cyclic equations are both products of special relativity itself, and both stem from the equation of helicity. This means that the symmetry of special relativity demands the existence of longitudinal solutions of Maxwell’s equations under all topological conditions. In particular, the fundamental spin component of the electromagnetic field is B, a longitudinal magnetic flux density which is free of phase and which is a topological invariant.