A Model of Topological Quantization of the Electromagnetic Field

Abstract

A recently proposed topological model of the electromagnetic field is described, which is based in the existence of electromagnetic knots, standard solutions of the Maxwell equations, characterized by the linking numbers n and m of the electric and magnetic vectors, the magnetic and electric helicities having the values h _mag = 2nћ, h _el = 2mћ. The model coincides locally with the classical Maxwell standard theory, but it is globally nonequivalent because its topological properties imply what is called a hidden nonlinearity: the fields span only a nonlinear subset of the solutions of a linear equation. Two consequences of the topological structure are important: the classical expression for the difference between the numbers of right handed and left handed photons is equal to n + m, having thus a topological interpretation, and the electric charge is quantized, the fundamental value being close to 14/3 times de electron charge.