Photon's Structure of Motion

Abstract

A free photon Hamiltonian is linearized using Pauli's matrices. Based on the correspondence of Pauli's matrices kinematics and the kinematics of spin operators, it has been proved that a free photon integral of motion is a sum of orbital momentum and spin momentum for a half-one spin. Linearized Hamiltonian represents a bilinear form of products of spin and momentum operators. Unitary transformation of this form results in an equivalent Hamiltonian, which has been analyzed by the method of Green's functions. The evaluated Green function has given possibility for interpretation of photon reflection as a transformation of photon to antiphoton with energy change equal to double energy of photon and for spin change equal to Dirac's constant. Since photon is relativistic quantum object the exact determining of its characteristics is impossible. It is the reason for series of experimental works in which photon orbital momentum, which is not integral of motion, was investigated. The exposed theory was compared to the mentioned experiments and in some elements the satisfactory agreement was found.