Hamiltonian formalism for dynamics of particles in MOG

ABSTRACT MOG as a modified gravity theory is designed to be replaced with dark matter. In this theory, in addition the metric tensor, massive vector field where each particle has charge proportional inertial mass and couples through four-velocity of particle. work, we present Hamiltonian formalism for dynamics particles theory. The advantage better understanding analysing massless particles. deviate from geodesics space–time photons follow geodesics. We also study Newtonian post-Newtonian regimes observational purposes. An important result that while lensing on large scales compatible observations, however deflection angle stellar size larger than general relativity. This can rule out unless introduce screening mechanism change effective gravitational constant near compact objects like stars.