  We extend the three-dimensional noncommutative relations of the positions and
momenta operators to those in the four dimension. Using the Bopp shift
technique, we give the Heisenberg representation of these noncommutative
algebras and endow the noncommutative parameters associated with the Planck
constant, Planck length and cosmological constant. As an analog with the
electromagnetic gauge potential, the noncommutative effect can be interpreted
as an effective gauge field, which depends on the Plank constant and
cosmological constant. Based on these noncommutative relations, we give the
Klein-Gordon (KG) equation and its corresponding current continuity equation in
the noncommutative phase space including the canonical and Hamiltonian forms
and their novel properties beyond the conventional KG equation. We analyze the
symmetries of the KG equations and some observables such as velocity and force
of free particles in the noncommutative phase space. We give the perturbation
solution of the KG equation.
