For a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group and (non-commutative) algebra representation, depending on the specific quantization map. We discuss the construction of the non-commutative Fourier transform and the non-commutative algebra representation, via the Duflo quantization map, for a system whose phase space is the cotangent bundle of the Lorentz group.

中文翻译：

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Lorentz 群的 Duflo 非交换傅里叶变换

对于相空间是李群的余切丛的量子系统，例如对于具有弯曲几何的特殊情况的系统，人们通常求助于李群的不可约表示的描述，其中（非-commutative) 相空间变量仍然是模糊的。但是，可以定义非交换傅里叶变换，将组和（非交换）代数表示交织在一起，具体取决于特定的量化图。我们通过 Duflo 量化图讨论了相空间是 Lorentz 群的余切丛的系统的非交换傅里叶变换和非交换代数表示的构造。