Path Integral Formalism of Klein-Gordon Oscillator Particle in Non- Commutative Phase Space

Abstract

In the non-commutative phase space based on introducing the parameters of deformation in the Heisenberg’s known relations, we shall use the path integral method for constructing exact solutions to Green’s function which is associated with the Klein-Gordon’s oscillator problem. Then, we shall clarify the expressions of energy spectrum and the wave function corresponding are similar to the problem of Klein-Gordon particle under a constant magnetic field in ordinary phase space. The limit cases are then deduced from small parameters of deformations.