Gauge interactions and the Galilean limit

TL;DR

This paper derives Galilean-invariant effective actions for matter and gauge fields by non-relativistic reduction of relativistic theories, including higher derivative corrections, revealing new relations in Galilean electrodynamics.

Contribution

It introduces a systematic method to obtain Galilean-invariant matter and gauge theories from relativistic models, including higher derivative terms, and uncovers novel relations in Galilean electrodynamics.

Findings

Derived Galilean-invariant Schrödinger and Pauli-Schrödinger theories from relativistic QED.

Established consistent non-relativistic reductions with higher derivatives.

Discovered new relations between electric and magnetic components in Galilean electrodynamics.

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 reductions have been consistently carried out once again. 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.