On Characterization of Non-commutative Minkowski Space Time

Several field theory models on κspace time have been constructed , using different techniques such as by F. Mejer and J Lukierski specially in, scalar field theory on κ-Minkowski space. It has been shown by S. Tanimutra that in the flat space time, Feynman approach and minimal coupling method are equivalent which is usefull to derive the general equation of motion for a charged particle. We discuss here the applicability of Feynman approach for the case of general relativity, resulting in the derivation of the geodesic equation. We generalize the procedure for κ-Minkowski space. We obtain here corrections to the geodesic equation due to the κ-deformation of space time , up to the first order in the deformation parameter. WE know that a relativistic particle of mass m and electric charge e is described by in 4D-Minkowski space, where in 4DMinkowski space, where τ is a parameter. Let us write the following relations Material Science Research India Vol. 9(1), 123-127 (2012)