TITLE: Infinite dimensional symplectic geometry
QUESTION [20 upvotes]: Could anyone comment on possible references concerning infinite dimensionsal symplectic manifolds?. I am mainly concerned with hilbert spaces, so i am not interested in the convenient analysis approach to the topic given, for instance, by Michor and collaborators,
More spectifically, I am interested in an infinite-dimensional analogue of the Marsden-Weinstein reduction and applications. I am specially concerned with its possible uses in quantum mechanics.
Thank you in advance.

REPLY [9 votes]: A standard way of going from a symplectic manifold to quantum mechanics is Fedosov quantization. Now if you want to do this in infinite dimension, that means you are interested in quantum field theory. A good place to start is the thesis by Giovanni Collini (a former student of Stefan Hollands) which develops such a Fedosov quantization in the QFT context.