Noncommutative Geometry and Symplectic Field Theory
  In this work we study representations of the Poincare group defined over symplectic manifolds, deriving the Klein-Gordon and the Dirac equation in phase space. The formalism is associated with relativistic Wigner functions; the Noether theorem is derived in phase space and an interacting field, including a gauge field, approach is discussed. 
R. G. G. Amorim, M. C. B. Fernandes, F. C. Khanna, A. E. Santana & J.   D. M. Vianna