Systematic approach to deriving equations of collective field theory to any order

Question

The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study of large N asymptotics (e.g. of matrix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.

This post imported from StackExchange Physics at 2017-01-21 16:19 (UTC), posted by SE-user Zoran Škoda

Comments

I dont know if this could help or if it's even relevant but page 17 here arxiv.org/pdf/gr-qc/9909037.pdf and archive.org/stream/arxiv-gr-qc9902064/gr-qc9902064_djvu.txt Let me know if these are useful or relevant. I am just a beginner.

This post imported from StackExchange Physics at 2017-01-21 16:19 (UTC), posted by SE-user CommaToast

Answer 1

I would suggest this book I think pages 29-30 offer some answers.

This post imported from StackExchange Physics at 2017-01-21 16:19 (UTC), posted by SE-user QuantumSerbian