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Non-abelian Gauge Symmetry for Fields in Phase Space: a Realization of the Seiberg-Witten Non-abelian Gauge Theory

  • J. S. Cruz-Filho
  • R. G. G. Amorim
  • F. C. Khanna
  • A. E. Santana
  • A. F. SantosEmail author
  • S. C. Ulhoa
Article

Abstract

The Seiberg-Witten formalism has been realized as an electrodynamics in phase space (associated to the Dirac equation written in phase space) and this fact is explored here with non-abelian gauge group. First, a physically heuristic presentation of the Seiberg-Witten approach is carried out for non-abelian gauge in order to guide the calculation procedures. These results are realized by starting with the Lagrangian density for the free Dirac field in phase space. Then a field strength is derived, where the non-abelian gauge group is the SU(2), corresponding to an isospin (non-abelian) field theory in phase space. An application to nucleon is then discussed.

Keywords

Non-abelian gauge theory Phase space Seiberg-Witten formalism 

Notes

Acknowledgments

This work was partially supported by FAP-DF of Brazil. The work by AES and AFS is supported by CNPq of Brazil.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Secretaria de Estado de Educação de Mato GrossoCuiabáBrazil
  2. 2.International Center of Physics, Instituto de FísicaUniversidade de BrasíliaBrasiliaBrazil
  3. 3.Faculdade GamaUniversidade de BrasíliaBrasiliaBrazil
  4. 4.Physics Department, Theoretical Physics InstituteUniversity of AlbertaEdmontonCanada
  5. 5.TRIUMFVancouverCanada
  6. 6.Instituto de FísicaUniversidade Federal de Mato GrossoCuiabáBrazil
  7. 7.Department of Physics and AstronomyUniversity of VictoriaVictoriaCanada

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