Quantum Theory of Hydrodynamic Currents

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Abstract
The current-current commutation relations, satisfied by the microscopic currents, are used to determine the algebraic properties of the basic hydrodynamic variables in quantum hydrodynamics. Using a Hamiltonian as suggested by the microscopic theory, a new system of hydrodynamic equations is obtained which contained the classical hydrodynamic equations including vortex motion in the classical limit. The concept of the fluid velocity in quantum mechanics of many particles is also discussed.

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