The scheme of Kadanoff and Baym is shown to be useful for the rigorous derivation of Bloch or Boltzmann equations for spin systems. The scheme is applied to a system of conduction electrons in a metal interacting via an exchange interaction $J$ with a low density of local spins. The coupled Bloch equations appropriate to conduction-electron spin resonance are derived rigorously to second order in $J$. The prominent features of the derived equations are that (i) the disturbed magnetizations are shown to relax to the instantaneous local equilibrium magnetization with the result that correct static susceptibilities are obtained, (ii) the instantaneous magnetizations are not proportional to the effective magnetic fields causing the magnetizations to precess, and (iii) the equations are consistent with conservation of the total magnetization.

• Received 15 June 1971

DOI:https://doi.org/10.1103/PhysRevB.6.3189