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General covariance and harmonic maps.

S Sternberg1

  • 1Department of Mathematics, Harvard University, Cambridge, MA 02138, USA.

Proceedings of the National Academy of Sciences of the United States of America
|August 4, 1999
PubMed
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General covariance principles were applied to determine harmonic map conditions. The study details how Yang-Mills fields modify these harmonic map equations.

Area of Science:

  • Differential Geometry
  • Theoretical Physics

Background:

  • Harmonic maps are fundamental geometric objects.
  • General covariance is a key principle in modern physics.

Purpose of the Study:

  • To derive conditions for harmonic maps using general covariance.
  • To investigate modifications to harmonic map equations in the presence of Yang-Mills fields.

Main Methods:

  • Application of the principle of general covariance.
  • Derivation of harmonic map equations.
  • Analysis of Yang-Mills field influence.

Main Results:

  • Established the conditions for a map to be harmonic.
  • Described specific modifications to the harmonic map equations.

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Conclusions:

  • The study provides a framework for understanding harmonic maps in curved spacetimes.
  • The findings are relevant for theories involving gauge fields and geometric structures.