# The Orbital and Spin Momenta of Light

by kderakhshani
Tags: angular momentum, light, momenta, optics, orbital, spin
 P: 10 Hi everybody, In most classical or quantum optics texts an angular momentum is considered for the EM radiation as the following: $J = ε_0 ∫_V r × [E(r, t) × B(r, t)] d^3 r$ Then it is claimed that: "Using the usual formula for a double vector product and integrating by parts, bearing in mind the assumption that the fields are zero at the surface of volume V introduced for the mode expansion, one finds that JR can be written as a sum of two terms: $J = L + S ,$ given by $L = ε_0 ∑_{j=(x,y,z)} ∫d^3r Ej (r, t)(r × ∇)Aj (r, t) ,$ $S = ε_0 ∫d^3r E(r, t) × A(r, t)$ " Would you please help me derive them? Thank you