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Covariant coordinate transformations on noncommutative space.

R Jackiw1, S-Y Pi

  • 1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA.

Physical Review Letters
|March 23, 2002
PubMed
Summary
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This study defines gauge-covariant coordinate transformations for noncommuting spaces using the Seiberg-Witten equation. This method extends existing techniques for commuting coordinates in theoretical physics.

Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Noncommutative Geometry

Background:

  • Coordinate transformations are fundamental in physics, typically defined on commutative spaces.
  • Noncommutative spaces present challenges for standard geometric and transformation definitions.
  • The Seiberg-Witten equation is a powerful tool in gauge theory and geometry.

Purpose of the Study:

  • To develop a method for defining gauge-covariant coordinate transformations on noncommuting spaces.
  • To generalize existing constructions of coordinate transformations to a noncommutative setting.
  • To explore the application of the Seiberg-Witten equation in this context.

Main Methods:

  • Utilizing the Seiberg-Witten equation as a foundational element.

Related Experiment Videos

  • Developing a framework for gauge covariance on noncommutative manifolds.
  • Adapting techniques from commutative geometry to the noncommutative case.

    • Main Results:

    • A concrete construction for gauge-covariant coordinate transformations on noncommuting spaces is presented.
    • The proposed method successfully generalizes established results for commuting coordinates.
    • The Seiberg-Witten equation is shown to be instrumental in this generalization.

    Conclusions:

    • The defined transformations provide a consistent framework for studying gauge theories on noncommuting spaces.
    • This work opens new avenues for research in noncommutative geometry and its physical applications.
    • The generalization offers a powerful tool for theoretical physicists working with noncommutative structures.