Dynamical properties of Heisenberg antiferromagnets: comparison of equation of motion and diagrammatic techniques

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Abstract
One and two magnon correlations are examined within the framework of standard perturbation theory using a Hollstein-Primakoff spin wave representation. Within the RPA this method reproduces the results obtained by the equation of motion technique in ibid., vol.6, 323 (1973), provided it is carried out in a certain selfconsistent way. A step by step comparison of the two methods throws new light onto the physical implications involved in the different approximations which seem to be favoured by the two techniques. The present method has in general an advantage over the equation of motion method in casting its results in terms which are easily physically interpretable. This allows the derivation of a simple expression for the neutron scattering cross section in terms of merely three q- omega dependent functions which describe certain free two-magnon correlation functions.