Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras

Topology Change for Fuzzy Physics: Fuzzy Spaces as Hopf Algebras
复制标题

模糊物理的拓扑变化：作为 Hopf 代数的模糊空间

DOI：
--
复制
发表时间：
2003
期刊：
影响因子：
--
通讯作者：
S. Kurkcuoglu
S. Kurkcuoglu
中科院分区：
--
文献类型：
--
作者：
A. P. Balachandran;S. Kurkcuoglu

文献摘要

被引文献

相似文献

模糊空间是通过量子化紧半单李群的伴随轨道而得到的。模糊球从量子化S^2中产生，并以这种方式与群SU（2）相关联。它们对于正则化量子场论和用非对易流形模拟时空是有用的。我们表明，模糊空间是Hopf代数，实际上有更多的结构比后者。因此它们是量子对称性的候选者。利用它们的广义Hopf代数结构，我们也可以对一个模糊空间分裂为多个模糊空间的过程进行建模。例如，我们可以讨论角动量J的模糊球分裂成角动量K和L的模糊球的量子跃迁。
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field theories and modeling spacetimes by non-commutative manifolds. We show that fuzzy spaces are Hopf algebras and in fact have more structure than the latter. They are thus candidates for quantum symmetries. Using their generalized Hopf algebraic structures, we can also model processes where one fuzzy space splits into several fuzzy spaces. For example we can discuss the quantum transition where the fuzzy sphere for angular momentum J splits into fuzzy spheres for angular momenta K and L.