Topological photon, spin, and Euclidean group E(2)

Abstract: The proposition that photon is a topological object (J. Math. Phys. 49, 032303, 2008) is given rigorous foundation based on pure vector field theory independent of the electromagnetic fields. Holomorphy of 4-dimensional space-time and the nature of topological obstructions are investigated to articulate singular vortex model for photon. The utility of the Euclidean symmetry group is discussed in detail for the proposed photon model.