If ω is a closed G -invariant 2-form and μ is a moment map, we obtain necessary and sufficient conditions for equivariant prequantizability that can be computed in terms of the moment map μ. Our main result is that G -equivariant prequantizability is related to the fact that the moment map μ should be quantized for certain vectors on the Lie algebra of G . We also compute the obstructions to lift the action of G to a prequantization bundle of ω. Our results are valid for any compact and connected Lie group G .

中文翻译：

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等变预量化和矩图

如果ω是闭合的G不变2形式，而μ是矩图，我们就可以根据矩图μ计算出等变预量化的必要和充分条件。我们的主要结果是，G等量可量化性与以下事实有关：应针对G的Lie代数上的某些矢量对矩图μ进行量化。我们还计算了将G的作用提升到ω的预量化束的障碍。我们的结果对于任何紧凑且连通的李群G都是有效的。