In the one-loop approximation we derive the equation of motion for aclassical scalar field \phi_c (t) with the back reaction of particle productionincluded. Renormalization of mass and couplings of \phi_c is done explicitly.The equation is non-local in time, but can easily be treated perturbatively ornumerically. For the weak trilinear coupling of the external field to theproduced particles, the new equation gives the same solution as the familiarone with the \Gamma \phi_c term. For a stronger coupling and other types ofcouplings the results are significantly different. The equation can be appliedto the universe heating by the inflaton decay and to spontaneous baryogenesis.
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