arXiv 2401.020072024-01-04hep-th

任意质量(A)dS$_4$粒子的旋量-螺旋性表示

Spinor-helicity representations of (A)dS$_4$ particles of any mass

Thomas Basile, Euihun Joung, Karapet Mkrtchyan, Matin Mojaza

备注：: 25 pages

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AI总结：

本文在双重对对应框架下，研究了四维(A)dS时空中任意质量粒子的旋量-螺旋性表示，确定了不同宇宙常数下对偶代数的结构，并探讨了其在描述大质量与部分无质量粒子及构建散射振幅对应物中的应用。

摘要：

在双重对对应框架下，研究了四维（反）德西特时空中大质量和部分无质量粒子的旋量-螺旋性表示。我们证明AdS群和dS群的对偶群（即“小群”）分别为$O(2N)$和$O^*(2N)$。当$N=1$时，对偶代数$\mathfrak{so}(2)\cong \mathfrak{so}^*(2) \cong \mathfrak{u}(1)$的生成元对应于螺旋度算符，该旋量-螺旋性表示描述了(A)dS$_4$中的无质量粒子。当$N=2$时，对偶代数由两个理想$\mathfrak{s}$和$\mathfrak{m}_Λ$组成。前一个理想$\mathfrak{s}\cong \mathfrak{so}(3)$固定粒子的自旋，而质量由后一个理想$\mathfrak{m}_Λ$决定，后者依宇宙常数为正、零或负分别同构于$\mathfrak{so}(2,1)$、$\mathfrak{iso}(2)$或$\mathfrak{so}(3)$。在宇宙常数为正即dS$_4$的情况下，旋量-螺旋性表示包含对应于主列表示的所有大质量粒子，以及对应于离散列表示的部分无质量粒子，仅排除了对应于互补列表示的轻质量大粒子。先前文献已探讨的零和负宇宙常数情形也被简略讨论。最后，我们考虑了在(A)dS群下不变的多线性螺旋度旋量形式，它可作为散射振幅的(A)dS对应物，并讨论了与平坦时空情形相比，(A)dS情形的技术差异与困难。

英文摘要：

The spinor-helicity representations of massive and (partially-)massless particles in four dimensional (Anti-) de Sitter spacetime are studied within the framework of the dual pair correspondence. We show that the dual groups (aka "little groups") of the AdS and dS groups are respectively $O(2N)$ and $O^*(2N)$. For $N=1$, the generator of the dual algebra $\mathfrak{so}(2)\cong \mathfrak{so}^*(2) \cong \mathfrak{u}(1)$ corresponds to the helicity operator, and the spinor-helicity representation describes massless particles in (A)dS$_4$. For $N=2$, the dual algebra is composed of two ideals, $\mathfrak{s}$ and $\mathfrak{m}_Λ$. The former ideal $\mathfrak{s}\cong \mathfrak{so}(3)$ fixes the spin of the particle, while the mass is determined by the latter ideal $\mathfrak{m}_Λ$, which is isomorphic to $\mathfrak{so}(2,1)$, $\mathfrak{iso}(2)$ or $\mathfrak{so}(3)$ depending on the cosmological constant being positive, zero or negative. In the case of a positive cosmological constant, namely dS$_4$, the spinor-helicity representation contains all massive particles corresponding to the principal series representations and the partially-massless particles corresponding to the discrete series representations leaving out only the light massive particles corresponding to the complementary series representations. The zero and negative cosmological constant cases, which had been addressed in earlier references, are also discussed briefly. Finally, we consider the multilinear form of helicity spinors invariant under (A)dS group, which can be served for the (A)dS counterpart of the scattering amplitude, and discuss technical differences and difficulties of the (A)dS cases compared to the flat spacetime case.

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