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Related Experiment Videos

Stability and gap phenomena for Yang-Mills fields.

J P Bourguignon1, H B Lawson, J Simons

  • 1Centre de Mathématiques, Ecole Polytechnique, F-91128 Palaiseau-Cedex, France.

Proceedings of the National Academy of Sciences of the United States of America
|April 1, 1979
PubMed
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Weakly stable Yang-Mills fields on the four-sphere are self-dual or anti-self-dual. Yang-Mills fields on larger spheres (n>5) are unstable, but stable examples exist for specific cases.

Area of Science:

  • Theoretical Physics
  • Differential Geometry
  • Mathematical Physics

Background:

  • Yang-Mills theory describes fundamental forces.
  • The stability of Yang-Mills fields is crucial for physical theories.
  • The four-sphere (S(4)) and higher-dimensional spheres (S(n)) are key manifolds in theoretical physics.

Purpose of the Study:

  • To investigate the stability and properties of Yang-Mills fields on spheres.
  • To determine conditions for self-duality and triviality of Yang-Mills fields.
  • To provide examples of stable Yang-Mills fields in specific geometric settings.

Main Methods:

  • Analysis of Yang-Mills fields on compact manifolds, specifically spheres.
  • Application of stability criteria and pointwise conditions.

Related Experiment Videos

  • Investigation of self-duality and anti-self-duality properties.

    • Main Results:

    • Weakly stable Yang-Mills fields of type SU(2) or SU(3) on S(4) must be self-dual or anti-self-dual.
    • Yang-Mills fields on S(n) for n >= 5 are generally unstable.
    • Pointwise conditions on the field strength imply triviality or specific structures for Yang-Mills fields on S(n).

    Conclusions:

    • The geometry of the sphere significantly impacts Yang-Mills field stability.
    • Specific pointwise conditions can rigorously constrain Yang-Mills fields to be trivial or exhibit particular forms.
    • The study provides a deeper understanding of Yang-Mills theory on curved spacetimes.