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Non-abelian Gauge Symmetry for Fields in Phase Space: a Realization of the Seiberg-Witten Non-abelian Gauge Theory |
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| Authors: | Cruz-Filho J. S. Amorim R. G. G. Khanna F. C. Santana A. E. Santos A. F. Ulhoa S. C. |
| Affiliation: | 1.Secretaria de Estado de Educação de Mato Grosso, 78049-909, Cuiabá, Mato Grosso, Brazil ;2.International Center of Physics, Instituto de Física, Universidade de Brasília, 70.910-900, Brasilia, DF, Brazil ;3.Faculdade Gama, Universidade de Brasília, 72444-240, Brasilia, DF, Brazil ;4.Physics Department, Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, T6G 2J1, Canada ;5.TRIUMF, 4004, Westbrook Mall, Vancouver, British Columbia, V6T 2A3, Canada ;6.Instituto de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso, Brazil ; |
| 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. |
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