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Vortices in He II, current algebras and quantum knots

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  • Rasetti, M.
  • Regge, T.

Abstract

A canonical quantization scheme is developed for vertices in superfluid He II, using Dirac's technique for constrained hamiltonian systems. Quantization introduces in the theory in natural way the structure of the infinite Lie algebra of incompressible flows. We argue that all the topological invariants of the vortex, considered as a knot, can be regarded as observables of the system. Finally unitary representations of measure preserving flows on R3 and current algebra are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:80:y:1975:i:3:p:217-233
    DOI: 10.1016/0378-4371(75)90105-3
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    Cited by:

    1. 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.
    2. Holm, Darryl D., 2003. "Rasetti–Regge Dirac bracket formulation of Lagrangian fluid dynamics of vortex filaments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 53-63.

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