论文标题
具有正能的模糊共形组SU（2,2）的一些振荡表示
Some oscillatory representations of fuzzy conformal group SU(2,2) with positive energy
论文作者
论文摘要
我们将相对论的模糊空间构建为函数的非共同代数，纯粹的结构和抽象坐标是作用于Hilbert Space $ \ Mathcal {H h} _f $的差异和ni径（C/A）操作员。使用这些振荡器，我们代表了包含代数$ su（2,2）$（包含描述物理可观察物的操作员，这些操作员由运营商通过此类功能和重建辅助Hilbert Space $ \ Mathbert $ \ Mathcal cancal cancal of to and a and CALCAL {然后，我们在此类空间上分析国家，并证明它们是增强不变的。最终，我们构建了两类不可约为的$ su（2,2）$代数，\ textit {fextit {fextiT {fextIt} dimension $ d $（[1））：（模糊的大型田地是两个doubleton表示的直接乘积，该磁场是由两组C/A算子构建的，分别是代数的基本和双重表示。
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.
