20.500.12556/RUL-180495 Algebraic structure of the gradient expansion in linearized classical hydrodynamics In this work, we systematically treat the ambiguities that generically arise in the gradient expansion of any hydrodynamic theory. While these ambiguities do not affect the physical content of the equations, they induce two types of transformations in the space of transport coefficients. The first type is known as the “frame” transformations, and amounts to field redefinitions. The second type, which we introduce and formalize here, we term the “on-shell” transformations. This identifies equivalence classes of hydrodynamic theories that provide an equally valid low-energy description of the underlying microscopic theory. We show that in any (classical) theory of hydrodynamics (at arbitrary order in derivatives), the action of such transformations on the dispersion relations and two-point correlation functions is universal. We explicitly construct invariants which can then be matched to a microscopic theory. Among them are, expectedly, the low-momentum expansions of the hydrodynamic modes. The (unphysical) gapped modes can, however, be added or removed at will. Finally, we show that such transformations assign a nilpotent Lie group to every hydrodynamic theory, and discuss the related algebraic properties underlying classical hydrodynamics. hydrodynamics linear response theory heavy-ion collisions hidrodinamika teorija linearnega odziva trki težkih ionov true false true Angleški jezik Slovenski jezik Članek v reviji 2026-03-10 14:44:25 2026-03-10 14:44:27 2026-03-11 04:38:32 0000-00-00 00:00:00 2026 0 0 Str. 065006-1-065006-21 iss. 6 Vol. 113 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 53 2470-0010 10.1103/hkzq-b2ph 271162371 hkzq-b2ph.pdf hkzq-b2ph.pdf 1 917471BD58674F6101F9E43B355A9C0C 6f81e7da5cf05ee9c9a374b628e62102075e776de94961bcbc79817a9abb755e 1a291ca3-1c88-11f1-a1ba-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=229943 https://journals.aps.org/prd/abstract/10.1103/hkzq-b2ph 0 10589866-1c88-11f1-a1ba-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=229942 Fakulteta za matematiko in fiziko 0 0 0