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Current algebras and liquid helium

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  • Albertin, Uwe K.
  • Morrison, Harry L.

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.

Suggested Citation

  • Albertin, Uwe K. & Morrison, Harry L., 1989. "Current algebras and liquid helium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 159(2), pages 188-220.
    • Handle: RePEc:eee:phsmap:v:159:y:1989:i:2:p:188-220
    DOI: 10.1016/0378-4371(89)90566-9
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    References listed on IDEAS

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    1. Rasetti, M. & Regge, T., 1975. "Vortices in He II, current algebras and quantum knots," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 80(3), pages 217-233.
    2. Cohen, I. Bernard, 1956. "Studies in Ancient Technology. By R. J. Forbes. Leiden, E. J. Brill, 1955. 3 vols. Pp. x + 194; vi + 215; vi + 268. 52 guilders," Business History Review, Cambridge University Press, vol. 30(2), pages 238-240, June.
    3. Morrison, Rodney J, 1969. "Teaching Hour-Load Assignments in Economics Departments in Larger Institutions Revisited," American Economic Review, American Economic Association, vol. 59(5), pages 960-962, December.
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