Current-Algebra Approach to Landau's Quantized Hydrodynamics

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Abstract
Landau's quantized hydrodynamics is derived from the microscopic Hamiltonian, which is written in terms of the density and velocity operators. In Euler's equation for the velocity operator, the force per unit mass has a form different from Landau's and is given explicitly in terms of the two-body potential. A quantum pressure term, which does not occur in Landau's theory, also appears. New realizations of the density and velocity operators are given which satisfy the commutation relations, but must act in a Hilbert space larger than Fock space. It is shown that the formalism is without meaning in Fock space owing to the nonexistence of certain operators.