Non-abelian gauge symmetry for fields in phase space: a realization of the Seiberg-Witten non-abelian gauge theory

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.

26 pages, accepted for publication in IJTP

References in corpus (8)

• Non-Commutative Complete Mellin Representation for Feynman Amplitudes
• Commutative limit of a renormalizable noncommutative model
• Noncommutative Geometry and Symplectic Field Theory
• Dispersion Relations in Noncommutative Theories
• Realization of the Noncommutative Seiberg-Witten Gauge Theory by Fields in Phase Space
• Unification of gravity and quantum field theory from extended noncommutative geometry
• Hénon-Heiles Interaction for Hydrogen Atom in Phase Space
• Symplectic Dirac Equation