Abstract
Bosonic mean-field asymptotics has long been known to be formally a semiclassical problem in infinite dimension. A number of works in recent years have focused on adapting semiclassical techniques to infinite dimension, not necessarily to deal solely with the mean field. After discussions with a number of colleagues, including Steve Zelditch, I propose to give a quick overview of what works and what doesn't work exactly as in finite dimension. First, I'll outline a few simple models that fit, directly or not so directly, into a mean-field framework. Then I'll look at different approaches and discuss the subtleties of infinite dimension. Steve Zelditch asked me : " Is there an Egorov theorem in infinite dimension ? ". My answer is : " No and yes ". I'll explain.
