Selfconsistent approximations for the Heisenberg model

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Abstract
The Baym-Kadanoff method for generating conserving approximations is generalized so that it may be applied to the drone-fermion representation of the spin 1/2 Heisenberg model. It is shown that the generalized procedure gives approximations in which the correlation functions preserve (i) commutation rules between spin operator components, (ii) conservation laws for the total spin, (iii) the relation between long wavelength longitudinal susceptibility and the field derivative of the magnetization, and (iv) the isotropy of the system in the paramagnetic phase in zero field. Moreover the approximate free energy is stationary with respect to variations of the Green function, and its derivatives with respect to external parameters are correctly related to the correlation functions.