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


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.



Hydrogen Neural Network Statistical Physic Hydrogen Atom Angular Momentum 
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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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