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Field Theoretic Approach to Hydrodynamics II. The Superfluid Hydrodynamics
Author(s) -
Ichiyanagi Masakazu
Publication year - 1991
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190390105
Subject(s) - physics , superfluidity , formalism (music) , lagrangian , invariant (physics) , mathematical physics , field (mathematics) , classical mechanics , theoretical physics , quantum mechanics , mathematics , pure mathematics , art , musical , visual arts
The first paper in this series developed a field‐theoretical approach to hydrodynamics. The objective of this second paper is to extend that formalism to superfluid hydrodynamics. Given the viewpoint adopted here, the fundamental objectives of the theory are the superfluid order‐parameter function, Ψ(x), the collective and the individual motions, in terms of which one can define Galilei invariants. Basic to the present theory is that the Schrödinger field Ψ(x) can by expressed in terms of the Galilei invariants (ϕ n (x), ϕ s (x)) and the phase ϕ(x) as φ(x) = exp {( im /h) ϕ(x)} F [ x : Ψ( x ), ϕ n ( x ), ϕ s ( x ), φ(x)] where the complex field φ(x) describes the individual motions (or is the asymptotic field). A plausible Lagrangian density, which in invariant, under the Galilei boost with a constant velocity, then permits the derivation of the equation of motion for the order‐parameter.