First Order Galilean Superfluid Dynamics

TL;DR

This paper develops a first-order derivative expansion framework for Galilean superfluid dynamics, establishing a null superfluid system that corresponds to Galilean superfluids via null reduction, linking relativistic and non-relativistic theories.

Contribution

It introduces a null superfluid model that maps onto Galilean superfluid dynamics, providing a new relativistic perspective and formalism for analyzing non-relativistic superfluid behavior.

Findings

Null superfluid corresponds to Galilean superfluid via null reduction.

Constructed first-order derivative expansion for Galilean superfluid.

Established offshell formalism adapted for null superfluids.

Abstract

We study dynamics of (anomalous) Galilean superfluid up to first order in derivative expansion, both in parity-even and parity-odd sectors. We construct a relativistic system -- null superfluid, which is a null fluid (introduced in [arXiv:1509.04718]) with a spontaneously broken global $U(1)$ symmetry. A null superfluid is in one to one correspondence with Galilean superfluid in one lower dimension, i.e. they have same symmetries, thermodynamics, constitutive relations and are related to each other by a mere choice of basis. The correspondence is based on null reduction, which is known to reduce the Poincar\'{e} symmetry of a theory to Galilean symmetry in one lower dimension. To perform this analysis, we use offshell formalism of (super)fluid dynamics, adopting it appropriately to null (super)fluids.