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Algebraic Shells and the Interacting Boson Model of the Nucleus

In: Symmetries in Science VIII

Author

Listed:
  • Bruno Gruber

    (Southern Illinois University at Carbondale in Niigata Nakajo
    Arnold Sommerfeld Institute for Mathematical Physics Technical University of Clausthal)

Abstract

It is well known that, for the simplest possible case of a shell (spin s=1/2, orbital angular momentum I=0), the four shell states transform according to the smallest spin representation (1/2,1/2) of the algebra so(5). In this article it is shown that, within the (space of the) Clifford algebra associated with the fernnion operators, an algebraic shell can be found which is a generalization of the standard shell. The algebraic shell states go over into the standard shell states on the quotient space of the Clifford algebra with respect to a left ideal generated by the identity operator 1 (which corresponds to the standard vacuum state).

Suggested Citation

  • Bruno Gruber, 1995. "Algebraic Shells and the Interacting Boson Model of the Nucleus," Springer Books, in: Bruno Gruber (ed.), Symmetries in Science VIII, pages 173-192, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-1915-7_14
    DOI: 10.1007/978-1-4615-1915-7_14
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