R^d上（保体积）作用的量子化
Quantization of (volume-preserving) actions on R^d
摘要：
我们将h-形式幂级数空间上的（形式）表示空间与Rd上的光滑函数空间中的系数（我们称之为量子化）与Rd上的群的作用（通过光滑同态）相关联。如果作用量进一步保持体积，则这些量化可以通过有界h相关傅里叶积分算子实现为Rd上平方可和函数的么正表示，正式情况对应于极限h趋于零的渐近性。我们构建DGAs控制这些量化，并证明存在性和刚性的结果。
英文摘要：
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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