Unified Spin Electrodynamics of Maxwell Bosons and Dirac Fermions

Bosons and fermions show similar spin and angular momentum textures. Studies of the spin for the surface plasmon polaritons (SPPs) propagating at the interface of an insulator and a metal, as well as the solutions of the Dirac equation propagating at the interface of a positive and negative fermionic mass media (known as the Jackiw-Rebbi problem (JRP) ), show that both photons and fermions in these structures have fully transverse spin and form a momentum-decay-spin triplet. By solving Maxwell equations for bosons and Dirac equation for fermions we have derived these fundamental properties and have shown that they make consistent connection to the experimental results. We have also studied these spin properties in the cylindrical problems of an optical fiber (OF) for bosons, as well as the cylindrical problem of a Dirac wire (DW) for fermions. We have shown that the bosons in OF and fermions in DW show very similar spin and angular momentum textures with longitudinal and transverse spin components that are locked to their respective perpendicular component of the momentum. Our results present an important platform for the study of spin and angular momenta by making accurate predictions about the spin properties of bosons (fermions) by studying the spin of fermions (bosons).