Current algebras and liquid helium

Uwe K. Albertin and Harry L. Morrison

Physica A: Statistical Mechanics and its Applications, 1989, vol. 159, issue 2, 188-220

Abstract: Several theories for elementary excitations in liquid 4He are examined within the formalism of the nonrelativistic current algebra. We make use of the Helmholtz decomposition for the current operator, and an appropriate collective approximation to the algebra. The Bogoliubov spectrum is obtained, as has been done previously. An appropriate rescaling of the phonon operators then yields the Landau condition for superfluid flow. The transverse part of the Hamiltonian yields the Hamiltonian for vortex-vortex interactions in three dimensions. Examination of the current operators under the Helmholtz decomposition yields the operators describing a quantum vortex, first given by Rasetti and Regge, and their theory follows directly. Further examination of the smeared operators yields the roton theory of Feynman and Feynman and Cohen, which we modify using the Helmholtz decomposition.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:159:y:1989:i:2:p:188-220

DOI: 10.1016/0378-4371(89)90566-9

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