  Symplectic unitary representations for the Poincar\'{e} 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.
