Foundations of Physics

, Volume 13, Issue 1, pp 51–59 | Cite as

Angular-momentum theory and projective geometry

  • B. R. Judd
Invited Papers Dedicated to Eugene Paul Wigner

Abstract

The Desarguesian nature of angular-momentum theory is illustrated by drawing correspondences between relations satisfied by then-j symbols and various collinearity properties of the appropriate diagrams. No examples of Pappus' theorem have been found. A relation is suggested between the operations of angular-momentum theory and Hilbert's constructions for the addition and multiplication of points on a line.

Keywords

Projective Geometry Collinearity Property 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. R. Edmonds,Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, N.J., 1957).Google Scholar
  2. 2.
    A. P. Yutsis, I. B. Levinson, and V. V. Vanagas,The Mathematical Apparatus of the Theory of Angular Momentum (Monson, Jerusalem, 1962).Google Scholar
  3. 3.
    A. P. Jucys and A. A. Bandzaitis,Theory of Angular Momentum in Quantum Mechanics (Mokslas, Vilnius, 1977).Google Scholar
  4. 4.
    U. Fano and G. Racah,Irreducible Tensorial Sets (Academic Press, New York, 1959), App. I.Google Scholar
  5. 5.
    G. de B. Robinson,Foundations of Geometry (University of Toronto Press, Toronto, 1963).Google Scholar
  6. 6.
    B. R. Judd,Operator Techniques in Atomic Spectroscopy (McGraw-Hill, New York, 1963), p. 92.Google Scholar
  7. 7.
    G. de B. Robinson,J. Math. Phys. 11, 3428 (1970).Google Scholar
  8. 8.
    L. C. Biedenharn and J. D. Louck,The Racah-Wigner Algebra in Quantum Theory: Encyclopedia of Mathematics and Its Applications (ed. G.-C. Rota), Vol. 9 (Addison-Wesley, New York, 1981).Google Scholar
  9. 9.
    D. Hilbert,Foundations of Geometry (Open Court, La Salle, Illinois, 1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1983

Authors and Affiliations

  • B. R. Judd
    • 1
  1. 1.Physics DepartmentThe Johns Hopkins UniversityBaltimore

Personalised recommendations