Non-Relativistic BMS algebra

TL;DR

This paper constructs two non-relativistic versions of the infinite-dimensional BMS algebra in four dimensions by contraction, extending the Bargmann algebra and realizing it through free Schrödinger fields.

Contribution

It introduces two novel non-relativistic $ ext{BMS}_4$ algebra candidates and provides a canonical realization using free Schrödinger fields.

Findings

Two candidate non-relativistic $ ext{BMS}_4$ algebras constructed.

Algebras are infinite-dimensional extensions of the Bargmann algebra.

Canonical realization achieved via Fourier modes of a free Schrödinger field.

Abstract

We construct two possible candidates for the non-relativistic $\mathfrak{bms}_4$ algebra in 4 space-time dimensions by contracting the original relativistic $\mathfrak{bms}_4$ algebra. The $\mathfrak{bms}_4$ algebra is infinite-dimensional, and it contains the generators of the Poincar\'e algebra, together with the so-called super-translations. Similarly, the proposed $\mathfrak{nrbms}_4$ algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realisation of one these algebras in terms of the Fourier modes of a free Schr\"odinger field, mimicking the canonical realisation of the relativistic $\mathfrak{bms}_4$ algebra using a free Klein-Gordon field.