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Green's Functions and Superfluid Hydrodynamics

### Abstract

The two‐fluid hydrodynamics of Landau and Tisza is related to the thermodynamicGreen's function formulation of the many‐body problem. A specific approximation for the self‐energies yields directly the superfluidhydrodynamics in the limit of slow space and time variation. The approximation chosen is the simplest possible form for the self energies which includes the effects of collisions and which also satisfies the differential conservation laws for the mass, momentum, and energy. Of course these self energies are not adequate for a realistic description of ^{4}He. Nonetheless the structure of this model may provide some insight into the exact theory. For example, in the model employed here the self‐energies and Green's functions obey several integral identities which are utilized in the derivation of the two‐fluid hydrodynamics, and which yield useful expressions for some thermodynamic quantities. It is speculated that the identities and the consequent expressions for the various thermodynamic quantities may have a wider range of validity than their derivation.

© 1965 The American Institute of Physics

Received 19 April 1965
Published online 22 December 2004