Comment on "Deformations, relaxation and broken symmetries in liquids, solids and glasses: a unified topological field theory"

TL;DR

This paper critiques a recent field-theoretical approach to classical liquids, arguing it incorrectly applies quantum concepts like phase relaxation and Goldstone bosons, which are not relevant to classical hydrodynamics.

Contribution

The paper clarifies the inapplicability of quantum formalism and Goldstone bosons to classical liquids, emphasizing the importance of particle-number conservation and density fluctuations.

Findings

Quantum formalism does not apply to classical liquids.

Goldstone bosons are not present in classical liquids.

Hydrodynamic sound arises from conservation laws, not broken symmetries.

Abstract

We discuss a field-theoretical approach to liquids, solids and glasses, published recently [Phys.Rev.E {\bf105}, 034108 (2022)], which aims to describe these materials in a common quantum formalism. We argue that such quantum formalism is not applicable to classical liquids, and the results presented, which rely heavily on the concept of phase relaxation borrowed from quantum fluids, contradict the known hydrodynamic theory of classical liquids. In particular, the authors miss the important particle-number conservation law and the density fluctuations as hydrodynamic slow variable. Instead, the authors invoke Goldstone bosons as elementary hydrodynamic excitations. We point out that in a classical liquid there are no broken continuous symmetries and consequently no Goldstone bosons. The authors claim that the Goldstone bosons would be responsible for the existence of sound in liquids, instead of resulting from combined particle-number and momentum conservation, a fact well documented in fluid-mechanics textbooks.