We have built a noncommutative unitary gauge group model preserving translation invariance. It describes the interaction of the Dirac field with the gauge field. The interaction term is expanded as a power series resulting from the introduction of the inverse covariant derivative. The consistency of the model is sustained by the fact that the Ward identity holds at tree level. The pure Yang–Mills action, including the fixing term and the Faddeev–Popov ghost term were constructed. It is striking that the commutator of our covariant derivative contained the torsion tensor, in addition to the field strength from which the Yang–Mills action was built.

中文翻译：

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平移不变 U(N) 阻尼非交换规范模型的构建

我们建立了一个保持平移不变性的非交换酉规范群模型。它描述了狄拉克场与规范场的相互作用。由于引入了逆协变导数，交互项被扩展为幂级数。Ward 身份在树级别保持这一事实维持了模型的一致性。构建了包含固定项和 Faddeev-Popov 鬼项的纯 Yang-Mills 作用。令人惊讶的是，我们的协变导数的换向器包含扭转张量，以及建立杨-米尔斯作用的场强。