Helicity in Classical Electrodynamics and its Topological Quantization

Any divergenceless vector field defined in a 3-dimensional manifold defines an integral quantity called the helicity that measures the way in which any pair of integral lines curl to one another. In the case of Classical Electrodynamics in vacuum, the natural helicity invariant, called the electromagnetic helicity, has an important particle meaning: the difference between the numbers of rightand left-handed photons. In a topological model of Classical Electrodynamics, the helicity is topologically quantized, in a relation that connects the wave and particle aspects of the fields.