Gauge invariance and relativistic radiative transitions

摘要: The gauge invariance of the matrix elements electromagnetic interaction is a property that usually taken for granted. author describes unified derivation in which dependence on potentials are written exhibited explicitly. necessary and sufficient condition transition matrices all multipoles to be invariant longitudinal photons should vanish identically. This imposes conditions initial final wavefunctions automatically satisfied single-particle model but may not necessarily hold in, say, Hartree-Fock model. For electric dipole transitions, it shown Coulomb leads velocity form element nonrelativistic limit different choice needed give length form. Arguments advanced suggesting given privileged position approximate calculations atomic molecular probabilities.