Gauge invariant formulation of molecular electrodynamics and the multipolar Hamiltonian Original Research Article

The multipolar Hamiltonian has many advantages for describing the electrodynamics of nonrelativistic material systems. Usually it is derived by performing a canonical transformation on the minimal coupling Hamiltonian. We show that both the minimal coupling and the multipolar Hamiltonians are two forms of the same Hamiltonian corresponding to two choices of gauge: div A = 0 and r · A(r) = 0 respectively. We further discuss the use of the multipolar Hamiltonian in electronically extended systems.