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arXiv · 1202.0886

Quantization of (volume-preserving) actions on R^d

Benoit Dherin·Igor Mencattini
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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.

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Benoit Dherin, Igor Mencattini. 2012-08-16. Quantization of (volume-preserving) actions on R^d. https://arxiv.org/abs/1202.0886

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