Based on the gravity model as a gauge theory previously by the authors, the introduction of noncommutative structures in the very geometry is discussed and developed in a new different way. Taking into account a linear Lagrangian in curvature and considering a pair of coherent vectors responsible, among other things, for the symmetry breaking, the introduction of noncommutativity in the very structure of the geometry is achieved. The fact that the vectors are coherent states ensure not only the natural and total quantization of the model, but also the formulation of the noncommutative structure, in particular by the introduction of a star product from the convolutory properties thereof. This new star product, in a sharp contrast with other proposals, is independent of the Bargmann index or other parameters depending on the dimension of the representation of the structure group of the noncommutativity. We also explain in the same way that a matrix model, through the properties of these coherent vectors, can be easily formulated. The pros and cons of the implementation of star products versus a theory of matrices based on coset coherent states are briefly discussed.

中文翻译：

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动态对称性、相干态和非线性实现：迈向非对易引力

基于作者先前作为规范理论的引力模型，以一种新的不同方式讨论和发展了在非常几何中引入非对易结构。考虑到曲率中的线性拉格朗日，并考虑一对相干向量，其中包括对称性破坏，实现了在几何结构中引入非交换性。矢量是相干态这一事实不仅确保了模型的自然和完全量化，而且还确保了非对易结构的公式化，特别是通过引入来自其卷积性质的星积。这款新星产品，与其他提案形成鲜明对比，独立于 Bargmann 指数或其他参数，具体取决于非交换性结构群的表示维数。我们还以同样的方式解释了矩阵模型，通过这些相干向量的属性，可以很容易地制定。简要讨论了星积的实现与基于陪集相干态的矩阵理论的优缺点。