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

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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.

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References

  1. Michel, L.: C. R. Acad. sc. Paris272, 433 (1971)

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  9. Pegoraro, F.: On theSO(3) ×SO(3) Symmetry in hydrodynamical problems. Accademia Nazionale dei Lincei, Rendiconti Serie VIII, Vol. LII, Fasc. I, genn. 1972

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Authors and Affiliations

  1. Scuola Normale Superiore, Pisa, Italy

    Francesco Pegoraro

  2. Research Laboratory of Electronics, Massachusetts Institute of Technology, Room 26-213, 02139, Cambridge, Mass., USA

    Francesco Pegoraro

Authors
  1. Francesco Pegoraro
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Communicated by H. Araki

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Pegoraro, F. Three applications toSO(4) invariant systems of a theorem of L. Michel relating extremal points to invariance properties. Commun.Math. Phys. 42, 41–63 (1975). https://doi.org/10.1007/BF01609433

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  • DOI: https://doi.org/10.1007/BF01609433

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