Symplectic Dirac Equation

Abstract

Symplectic unitary representations for the Poincaré group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Klein-Gordon and Dirac equations are derived in phase space. As an application, we study the Dirac equation with electromagnetic interaction in phase space.

References in corpus (5)

• Noncommutative Geometry and Symplectic Field Theory
• The Weyl-Wigner-Moyal Formalism for Spin
• On the energy-momentum tensor in Moyal space
• Anomaly cancellation in three-dimensional noncommutative gauge theories
• Spin Description in the Star Product and the Path Integral Formalism

Cited by in corpus (1)

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