Gauge interactions and the Galilean limit

Abstract: The gauge invariant minimal couplings for a class of relativistic free matter fields with global symmetry (related to usual charge conservation) have been obtained by incorporating an iterative Noether mechanism. Non-relativistic reduction of both matter and gauge sectors of the obtained interacting theory is then performed simultaneously which in turn yield a set of new effective actions which are invariant under the Galilean relativistic framework. To be precise, we show that one can obtain the Schr\"odinger field theory coupled to Galilean electromagnetism from the scalar quantum electrodynamics theory. Higher derivative corrections have also been included for which the non-relativistic reduction has been carried out once again. Inclusion of higher derivative corrections is also consistent in this context. On the other hand, the action for quantum electrodynamics leads to the Galilean Pauli-Schr\"odinger theory where the gauge field is non-relativistic or Galilean. Further, some novel relations are found (in both the electric and magnetic limits) between various components appearing in the Galilean avatar of electrodynamics.