For a compact Lie group G we consider a lattice gauge model given by the G -Hamiltonian system which consists of the cotangent bundle of a power of G with its canonical symplectic structure and standard moment map. We explicitly construct a Fedosov quantization of the underlying symplectic manifold using the Levi–Civita connection of the Killing metric on G . We then explain and refine quantized homological reduction for the construction of a star product on the symplectically reduced space in the singular case. Afterwards we show that for $$G = {\mathrm {SU}}(2)$$ G = SU ( 2 ) the main hypotheses ensuring the method of quantized homological reduction to be applicable hold in the case of our lattice gauge model. For that case, this implies that the—in general singular—symplectically reduced phase space of the corresponding lattice gauge model carries a star product.

中文翻译：

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格规模型的变形量化和同调归约

对于紧李群 G，我们考虑由 G -Hamiltonian 系统给出的格子规范模型，该系统由 G 的幂的余切丛及其正则辛结构和标准矩图组成。我们使用 G 上的 Killing 度量的 Levi-Civita 连接显式地构造了底层辛流形的 Fedosov 量化。然后，我们解释并改进了在奇异情况下在辛约简空间上构造星积的量化同调约简。然后我们证明，对于 $$G = {\mathrm {SU}}(2)$$ G = SU ( 2 )，确保量化同调归约方法适用于我们的格子规范模型的主要假设成立。对于这种情况，