Quantization of (volume-preserving) actions on R^d
arXiv:1202.0886
Abstract
We associate a space of (formal) representations on the space of h-formal power series with coefficients in the space of smooth functions on Rd (which we call quantizations) with an action of a group on Rd by smooth diffeomorphisms. If the action is further volume preserving, these quantizations can be realized as unitary representations on square summable functions on Rd by bounded h-dependent Fourier integral operators, the formal case corresponding to the asymptotics in the limit h going to zero. We construct DGAs controlling these quantizations and prove existence and rigidity results for them.
21 pages. We added the notion of formal G-systems, associated with formal quantizations of smooth actions, and proved a corresponding existence and rigidity result