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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study of large N asymptotics (e.g. of matrix models). I have seen few cases where the equations for collective fields are derived; the equations are obtained using approximations and look more systematically understood by other methods than those available at dawn of collective field theory (i.e. since the works of Sakita and Jevicki).

Is there now a systematic method to derive collective field theory equations to any order in 1/N ? Also if the Yaffe's methods concerning coherent state methods in large N asymptotics are ever used in collective field theory ? The subject looks interesting for doing some work (I have some background in coherent state techniques), but I do not know what the current state of advance is.

EDIT: added a bounty to renew interest.

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