论文标题
$κ$定型的扩展Snyder模型的广义量子相位空间
Generalized quantum phase spaces for the $κ$-deformed extended Snyder model
论文作者
论文摘要
我们以代数的方式描述了$κ$成型的扩展Snyder模型，该模型取决于三个参数$β，κ$和$λ$，在适当的代数基础上，de Sitter代数代数$ {O}（O}（O}（O}（1，N）$。代数的换向关系包含一个参数$λ$，用于扰动扩展的计算。对于此类$κ$成型的扩展Snyder模型，我们考虑使用双重概括性型扇区的海森贝格双重，并根据上述三个参数提供相应的广义量子相空间。此外，我们为这些模型研究了一个替代的海森堡双重双重，而de Sitter组的功能代数为代数。在这两种情况下，我们都以$λ$的线性顺序计算了通用坐标和动量扇区之间交叉换向关系的公式。我们证明，在量子时空坐标的换向器中，量子构造的海森堡代数的动量元素是$κ$ - 定义产生的术语在$β$依赖性的$β$ eplught上占主导地位。
We describe, in an algebraic way, the $κ$-deformed extended Snyder models, that depend on three parameters $β, κ$ and $λ$, which in a suitable algebra basis are described by the de Sitter algebras ${o}(1,N)$. The commutation relations of the algebra contain a parameter $λ$, which is used for the calculations of perturbative expansions. For such $κ$-deformed extended Snyder models we consider the Heisenberg double with dual generalized momenta sector, and provide the respective generalized quantum phase space depending on three parameters mentioned above. Further, we study for these models an alternative Heisenberg double, with the algebra of functions on de Sitter group. In both cases we calculate the formulae for the cross commutation relations between generalized coordinate and momenta sectors, at linear order in $λ$. We demonstrate that in the commutators of quantum space-time coordinates and momenta of the quantum-deformed Heisenberg algebra the terms generated by $κ$-deformation are dominating over $β$-dependent ones for small values of $λ$.
