Galilei invariant theories. I. Constructions of indecomposable finite-dimensional representations of the homogeneous Galilei group: directly and via contractions

TL;DR

This paper classifies all indecomposable finite-dimensional representations of the homogeneous Galilei group that decompose into specific spin representations, and applies these to derive interaction terms for Galilean particles in electric fields.

Contribution

It provides a complete classification of certain Galilei group representations and connects them to physical interaction terms via contractions from Lorentz group representations.

Findings

Classified all relevant indecomposable finite-dimensional Galilei group representations.

Derived a general Pauli anomalous interaction term for Galilean particles.

Established connections between Galilei and Lorentz group representations through contractions.

Abstract

All indecomposable finite-dimensional representations of the homogeneous Galilei group which when restricted to the rotation subgroup are decomposed to spin 0, 1/2 and 1 representations are constructed and classified. These representations are also obtained via contractions of the corresponding representations of the Lorentz group. Finally the obtained representations are used to derive a general Pauli anomalous interaction term and Darwin and spin-orbit couplings of a Galilean particle interacting with an external electric field.