群场论的旋量和Voros星积：首次接触
Spinors and Voros star-product for Group Field Theory: First Contact
摘要：
在非对易几何的背景下，我们发展了李群SU（2）的群傅里叶变换。我们的方法是基于李代数su（2）的旋量Schwinger表示。它使我们能够证明，SU（2）群的非对易R^3空间对偶实际上是Moyal型的，并且在用旋量变量表示时具有Voros星积。最后，从量子引力的角度，我们讨论了这些新的工具的应用，自旋泡沫模型的群场论和它们的解释为非交换场论与量子变形对称性。
英文摘要：
In the context of non-commutative geometries, we develop a group Fourier transform for the Lie group SU(2). Our method is based on the Schwinger representation of the Lie algebra su(2) in terms of spinors. It allows us to prove that the non-commutative R^3 space dual to the SU(2) group is in fact of the Moyal-type and endowed with the Voros star-product when expressed in the spinor variables. Finally, from the perspective of quantum gravity, we discuss the application of these new tools to group field theories for spinfoam models and their interpretation as non-commutative field theories with quantum-deformed symmetries.
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