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

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