We build a model of the origin of physical constants, including masses and coupling constants. We consider the quantum correction of masses and coupling constants. Some exactly solved leading quantum corrections are given. In the model, the physical constant originates from a coupling between the matter field and a background field. We show that if such a background field as it should be in the real physical world is a quantum field, then the physical constant will have a space- and time-dependent quantum correction and will no longer be a constant. We build a scalar field model and a mechanics model. In these two models, we discuss the quantum correction of masses and coupling constants in the field framework and in the mechanics framework.
