Equation of motion of a classical scalar field with back reaction of produced particles

In the one-loop approximation we derive the equation of motion for a classical scalar field ϕ c (t) with the back reaction of particle production included. Renormalization of mass and couplings of ϕ c is done explicitly. The equation is non-local in time, but can easily be treated perturbatively or numerically. For the weak trilinear coupling of the external field to the produced particles, the new equation gives the same solution as the familiar one with the Γ ˙ ϕ c term. For a stronger coupling and other types of couplings the results are significantly different. The equation can be applied to the universe heating by the inflaton decay and to spontaneous baryogenesis.