扩展Snyder模型的关联实现
Associative realizations of the extended Snyder model
摘要：
通常与非交换几何的斯奈德模型相关联的星积是非结合的，这个性质阻止了一个正确的Hopf代数的构造。然而，通过将洛伦兹生成元和它们的共轭动量包含到代数中，可以引入一个定义良好的Hopf代数。在本文中，我们研究了这种扩展的Snyder时空的实现，并得到了一个Weyl序实现中的余积和扭曲以及结合星积，在非对易性参数的一阶。然后，我们将我们的结果扩展到最一般的实现扩展斯奈德时空，总是到一阶。
英文摘要：
The star product usually associated to the Snyder model of noncommutative geometry is nonassociative, and this property prevents the construction of a proper Hopf algebra. It is however possible to introduce a well-defined Hopf algebra by including the Lorentz generators and their conjugate momenta into the algebra. In this paper, we study the realizations of this extended Snyder spacetime, and obtain the coproduct and twist and the associative star product in a Weyl-ordered realization, to first order in the noncommutativity parameter. We then extend our results to the most general realizations of the extended Snyder spacetime, always up to first order.
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