The nonequilibrium statistical operator method is used to construct a two-velocity relativistic hydrodynamics of a quantum-field system with broken symmetry and complex scalar order parameter. The approach is based on model expansions of the operators (the energy-momentum tensor, the current density, etc.) used for statistical description of the system in the hydrodynamic stage. In the first part of the paper, these expansions are used to construct the statistical operator and the thermodynamics of a local-equilibriu m state. Below, we construct a quantum relativistic two-velocity hydrodynamics on the basis of first principles using Zubarev's nonequilibrium statistical operator method (11}. In Sec.2, we establish the connection between the 4-velocity of the motion of the ordered component with the gradient of the phase of the order parameter. In Sec.3 we note that the methods of (2-7) based on the use of unitary transformations in the Galileo group to obtain the equations of two-velocity hydrodynamics do not admit direct generalization to the relativistic domain. In this connection, we propose an approach based on model expansions of the energy-momentum tensor and the current density (and, possibly, other operators used for statistical des- cription of systems in the hydrodynamic stage). These expansions are then used in Sec.4 to construct the statistical operator and the thermodynamics of the local-equilibrium state. The transport relations and the hydrodynamic equations will be discussed in Part If. Below, we use a system of units in which c = l~ = k = 1. The signature of the metric tensor isThe nonequilibrium statistical operator method is used to construct a two-velocity relativistic hydrodynamics of a quantum-field system with broken symmetry and complex scalar order parameter. The approach is based on model expansions of the operators (the energy-momentum tensor, the current density, etc.) used for statistical description of the system in the hydrodynamic stage. In the first part of the paper, these expansions are used to construct the statistical operator and the thermodynamics of a local-equilibriu m state. Below, we construct a quantum relativistic two-velocity hydrodynamics on the basis of first principles using Zubarev's nonequilibrium statistical operator method (11}. In Sec.2, we establish the connection between the 4-velocity of the motion of the ordered component with the gradient of the phase of the order parameter. In Sec.3 we note that the methods of (2-7) based on the use of unitary transformations in the Galileo group to obtain the equations of two-velocity hydrodynamics do not admit direct generalization to the relativistic domain. In this connection, we propose an approach based on model expansions of the energy-momentum tensor and the current density (and, possibly, other operators used for statistical des- cription of systems in the hydrodynamic stage). These expansions are then used in Sec.4 to construct the statistical operator and the thermodynamics of the local-equilibrium state. The transport relations and the hydrodynamic equations will be discussed in Part If. Below, we use a system of units in which c = l~ = k = 1. The signature of the metric tensor is

Jan 1, 19830 citations

Quantum hydrodynamics of extended particles

A. I. Laptukhov

Russian Physics JournalSep 1, 19911 citation

On Higher-Form Fracton Hydrodynamics with Momentum Conservation

Ben Bobell, Rahul Nandkishore, Andrew Lucas

Momentum conservation is common in fluids, yet it may be incompatible with the hydrodynamics of theories with exotic conservation laws (such as fracton hydrodynamics) unless symmetries are spontaneously broken. Using the Martin-Siggia-Rose (MSR) effective field theory formalism, we develop a representation-theoretic framework for the hydrodynamics of translationally invariant systems with exotic conservation laws without spontaneous symmetry breaking. Under mild assumptions on the form of hydrodynamics, we show that such theories must satisfy two representation theoretic consistency conditions and a generalized Gauss's law constraint. Higher-form symmetries satisfy these conditions and we derive their ideal hydrodynamics; in three dimensions, the one-form case produces ideal non-relativistic magnetohydrodynamics. Finally, we prove that no other theories are compatible with momentum conservation in SO(3) nor SO( $d$ ), for sufficiently large odd $d$ .Momentum conservation is common in fluids, yet it may be incompatible with the hydrodynamics of theories with exotic conservation laws (such as fracton hydrodynamics) unless symmetries are spontaneously broken. Using the Martin-Siggia-Rose (MSR) effective field theory formalism, we develop a representation-theoretic framework for the hydrodynamics of translationally invariant systems with exotic conservation laws without spontaneous symmetry breaking. Under mild assumptions on the form of hydrodynamics, we show that such theories must satisfy two representation theoretic consistency conditions and a generalized Gauss's law constraint. Higher-form symmetries satisfy these conditions and we derive their ideal hydrodynamics; in three dimensions, the one-form case produces ideal non-relativistic magnetohydrodynamics. Finally, we prove that no other theories are compatible with momentum conservation in SO(3) nor SO($d$), for sufficiently large odd $d$.

arXiv:2610.26862Oct 19, 20260 citations

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