Multipole expansions of electromagnetic fields using Debye potentials

The Debye potentials are introduced by giving new derivations of the multipole expansions of the magnetostatic and electrostatic fields. Simplified derivations of the multipole expansions of the electrodynamic fields are then given. The radiated energy, momentum, and angular momentum are all calculated in the same manner, i.e., using the proper transport equations. The questions of uniqueness and completeness of the Debye potential representations of the fields are discussed. In the Appendices are collected together some useful vector field theorems and operator identities involving the angular momentum operator, and also simplified derivations of the spherical harmonic expansions of the static and dynamic Green functions.