弯曲卷积、Rieffel形变与量子场论的建立
Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories
摘要：
算符的弯曲卷积作为一种新的构造工具最近被引入量子物理的代数框架中。这里表明，这些卷积提供了具有R^n的自守作用的C*-动力系统的Rieffel严格变形的等距表示，只要后者以协变表示呈现。此外，该装置可用于相对论性量子场论的变形，通过调整的卷积闵可夫斯基空间的几何形状。由此产生的变形理论仍然符合相关的物理原理，它们的Tomita-Takesaki模数据与未变形理论的一致;但它们通常与未变形理论不等价，并表现出不同的物理解释。
英文摘要：
Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations of C*-dynamical systems with automorphic actions of R^n, whenever the latter are presented in a covariant representation. Moreover, the device can be used for the deformation of relativistic quantum field theories by adjusting the convolutions to the geometry of Minkowski space. The resulting deformed theories still comply with pertinent physical principles and their Tomita-Takesaki modular data coincide with those of the undeformed theory; but they are in general inequivalent to the undeformed theory and exhibit different physical interpretations.
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