The principle of symmetric criticality View Full Text


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Article Info

DATE

1979-10

AUTHORS

Richard S. Palais

ABSTRACT

It is frequently explicitly or implicitly assumed that if a variational principle is invariant under some symmetry groupG, then to test whether a symmetric field configuration ϕ is an extremal, it suffices to check the vanishing of the first variation of the action corresponding to variations ϕ + δϕ that are also symmetric. We show by example that this is not valid in complete generality (and in certain cases its meaning may not even be clear), and on the other hand prove some theorems which validate its use under fairly general circumstances (in particular ifG is a group of Riemannian isometries, or if it is compact, or with some restrictions if it is semi-simple). More... »

PAGES

19-30

References to SciGraph publications

  • 1977. Classical Lumps and Their Quantum Descendants in NEW PHENOMENA IN SUBNUCLEAR PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01941322

    DOI

    http://dx.doi.org/10.1007/bf01941322

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1032231386


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