Bundles of C*-algebras can be used to represent limits of physical theories whose algebraic structure depends on the value of a parameter. The primary example is the ℏ → 0 limit of the C*-algebras of physical quantities in quantum theories, represented in the framework of strict deformation quantization. In this paper, we understand such limiting procedures in terms of the extension of a bundle of C*-algebras to some limiting value of a parameter. We prove existence and uniqueness results for such extensions. Moreover, we show that such extensions are functorial for the C*-product, dynamical automorphisms, and the Lie bracket (in the ℏ → 0 case) on the fiber C*-algebras.

中文翻译：

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C*-代数束的扩展

C*-代数束可用于表示代数结构取决于参数值的物理理论的极限。主要的例子是ℏ → 0量子理论中物理量C*-代数的极限，以严格变形量化的框架为代表。在本文中，我们根据将一组 C*-代数扩展到某个参数的某个极限值来理解这种限制过程。我们证明了此类扩展的存在性和唯一性结果。此外，我们证明了这种扩展对于 C* 积、动态自同构和李括号（在ℏ → 0case) 在光纤 C*-代数上。