正能量Fuzzy共形群SU（2，2）的若干振动表示
Some oscillatory representations of fuzzy conformal group SU(2,2) with positive energy
摘要：
我们构造的相对论模糊空间作为一个非交换代数的功能与纯粹的结构和抽象的坐标是creaction和annihilation（C/A）运营商作用于Hilbert空间$\mathcal{H}_F$。使用这些振荡器，我们表示的共形代数$su(2,2)$（包含运营商描述的物理观测，产生助推，旋转，空间和共形平移，和膨胀）的运营商作用于这样的功能和重建一个辅助希尔伯特空间$\mathcal{H}_A$来描述这个行动。然后，我们分析这样的空间上的状态，并证明它们是升压不变的。最后，我们构造了两类具有\textit{half-integer}维数$d$的$su(2,2)$代数的不可约表示（[1]）：（i）经典模糊无质量场作为由一组C/A算子构造的$su(2,2)$在基本或酉不等价对偶表示中的双重表示;（ii）经典模糊有质量场作为由两组C/A算子构造的两个双重表示的直积。分别在代数的基本表示和对偶表示中的算子。
英文摘要：
We construct the relativistic fuzzy space as a non-commutative algebra of functions with purely structural and abstract coordinates being the creaction and annihilation (C/A) operators acting on a Hilbert space $\mathcal{H}_F$. Using these oscillators, we represent the conformal algebra $su(2,2)$ (containing the operators describing physical observables, that generate boosts, rotations, spatial and conformal translations, and dilatation) by operators acting on such functions and reconstruct an auxiliary Hilbert space $\mathcal{H}_A$ to describe this action. We then analyze states on such space and prove them to be boost-invariant. Eventually, we construct two classes of irreducible representations of $su(2,2)$ algebra with \textit{half-integer} dimension $d$ ([1]): (i) the classical fuzzy massless fields as a doubleton representation of the $su(2,2)$ constructed from one set of C/A operators in fundamental or unitary inequivalent dual representation and (ii) classical fuzzy massive fields as a direct product of two doubleton representations constructed from two sets of C/A operators that are in the fundamental and dual representation of the algebra respectively.
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