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Communications in Mathematical Physics

, Volume 42, Issue 1, pp 41–63 | Cite as

Three applications toSO(4) invariant systems of a theorem of L. Michel relating extremal points to invariance properties

  • Francesco Pegoraro
Article

Abstract

We consider a theorem due to Michel [1] which relates the invariance properties in peculiar directions in a linear space on which we represent a Lie groupG to the extremal points of an arbitrary smoothG-invariant function.

The group we are interested in isSO(4) and we apply the mathematical results to the following problems:
  1. i)

    mixed linear Stark Zeeman effect in a hydrogen atom,

     
  2. ii)

    perturbation of a finite Robertson-Walker metric,

     
  3. iii)

    gas evolutions preserving angular momentum and vorticity.

     

Keywords

Hydrogen Neural Network Statistical Physic Hydrogen Atom Angular Momentum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Michel, L.: C. R. Acad. sc. Paris272, 433 (1971)Google Scholar
  2. 2.
    Michel, L., Radicati, L.A.: Properties of the breaking of hadronic internal symmetry Ann. Physics66, (1971)Google Scholar
  3. 3.
    Pauli, W.: Z. Physik36, 336–363 (1926)Google Scholar
  4. 4.
    Robertson, H. P.: Ap. J.284, (1935)Google Scholar
  5. 4a.
    Robertson, H. P.: Ap J.83, 187–257 (1936)Google Scholar
  6. 4b.
    Walker, A. G.: Proc. Lond. Math. Soc.2, 42–90 (1936)Google Scholar
  7. 5.
    Minlos, G.: Representation of the rotation and Lorentz groups and their applications Vol. 99, Oxford: Pergamon Press 1963Google Scholar
  8. 6.
    Dyson, F.J.: Dynamics of a spinning gas cloud. J. Math. Mech.18, 91–101 (1968)Google Scholar
  9. 6a.
    Pegoraro, F.: On theSO(3) ×SO(3) Symmetry in hydrodynamical problems. Accademia Nazionale dei Lincei, Rendiconti Serie VIII, Vol. LII, Fasc. I, genn. 1972Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Francesco Pegoraro
    • 1
    • 2
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Research Laboratory of ElectronicsMassachusetts Institute of TechnologyCambridgeUSA

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