Hydrodynamics without boosts

TL;DR

This paper develops a comprehensive first-order hydrodynamic theory invariant under specific symmetries, applicable to various physical systems like graphene and flocking, and includes special cases with higher symmetry such as Lifshitz-invariant hydrodynamics.

Contribution

It constructs the most general first-order hydrodynamic theory with given symmetries, encompassing special cases like Lifshitz-invariant hydrodynamics and non-dissipative parity-preserving theories.

Findings

Derived the complete first-order Lifshitz-invariant hydrodynamics.

Identified classes of non-dissipative, parity-preserving theories.

Unified various hydrodynamic models under a common symmetry framework.

Abstract

We construct the general first-order hydrodynamic theory invariant under time translations, the Euclidean group of spatial transformations and preserving particle number, that is with symmetry group $\mathbb{R}_t\times$ISO$(d)\times$U$(1)$. Such theories are important in a number of distinct situations, ranging from the hydrodynamics of graphene to flocking behaviour and the coarse-grained motion of self-propelled organisms. Furthermore, given the generality of this construction, we are are able to deduce special cases with higher symmetry by taking the appropriate limits. In this way we write the complete first-order theory of Lifshitz-invariant hydrodynamics. Among other results we present a class of non-dissipative first order theories which preserve parity.