The partition function of the periodic Anderson model for an infinite U-term is represented by the path integral over the Grassmann variables for band s-electrons and supercoherent SU(2\1) variables for localized d-electrons. The effective electron action is obtained for d-electrons with a level E < 0 through the averaging of the thermal distribution over the s-electron trajectories. Due to the spinon-charge separation in the path integral over the d-variables, the low-temperature and spin mean-field approximations are introduced and are shown to lead to the adiabatic approximation suggested earlier. Non-linear dependence of the chemical potential μ on the electron concentration n < 1 is established for the narrow s-electron band w ≪ |E\ and the Kondo-like temperature behavior is found for n > 1 in wide w ≪ |E\ s-electron band.