Abstract We revisit the relation between the anomalies in four and six dimensions and the Chern-Simons couplings one dimension below.While the dimensional reduction of chiral theories is well-understood, the question which three and five-dimensional theories can come from a general circle reduction, and are hence liftable, is more subtle.We argue t

Spin angular momentum of a photon corresponds to a polarisation degree of freedom of lights, and such that various polarisation properties are coming from macroscopic manifestation of quantum-mechanical properties of lights.An orbital degree of freedom of lights is also manipulated to form a vortex of lights with orbital angular momentum, which is