Gauge-invariant Green function dynamics: A unified approach Original Research Article

We present a gauge-invariant description of Green function dynamics introduced by means of a generalized Peirels phase involving an arbitrary differentiable path in space–time. Two other approaches to formulating a gauge-invariant description of systems, the Green function treatment of Levanda and Fleurov [M. Levanda, V. Fleurov, J. Phys.: Condens. Matter 6 (1994) 7889] and the usual multipolar expansion for an atom, are shown to arise as special cases of our formalism. We argue that the consideration of paths in the generalized Peirels phase that do not lead to introduction of an effective gauge-invariant Hamiltonian with polarization and magnetization fields may prove useful for the treatment of the response of materials with short electron correlation lengths.