近日，比利时蒙斯大学的Thomas Basile与韩国庆熙大学的Euihun Joung以及TaeHwan Oh合作并取得一项新进展。经过不懈努力，他们揭示伴随轨道的明显协变世界线作用并进行第一部分的概述和向量描述。相关研究成果已于2024年1月5日在国际知名学术期刊《高能物理杂志》上发表。

该研究团队利用哈密顿约化，从等距群的共伴轨道出发，推导出自旋粒子的协变作用。他们证明了经典李群的定义条件可以被看作是产生另一个对偶李群的共伴轨道的哈密顿约束。对于(非齐次)正交群，对偶群是(中心扩展的非齐次)辛群。这定义了等距群和对偶李群的共伴轨道之间的辛对偶对应，其量子版本是约化对偶对相似物là la Howe。

研究人员明确地展示了不同的粒子种类是如何从庞加莱和(A)dS对称的共伴轨道分类中产生的。在庞加莱情况下，研究人员恢复了Wigner分类的数据，其中包括连续自旋粒子、(自旋)快子和具有消失动量的零粒子，以及通常的有质量和无质量自旋粒子。在(A)dS情况下，研究人员的分类结果不仅与文献中观察到的相应的幺正不可约表示的模式一致，而且包含了新的信息。

在dS中，研究人员发现了部分无质量自旋粒子的存在，但不存在连续自旋粒子、自旋快子和零粒子。AdS情况下粒子种类的多样性最大，除零粒子外，它具有庞卡罗莱对称的所有粒子种类，但还允许各种奇异实体，如连续粒子的单参数扩展和保形粒子存活在AdS的边界上。

值得注意的是，研究人员在研究中还发现了一大类存在于“双时间”AdS空间中的粒子，这些粒子包括质量和自旋互换作用的粒子。此外，他们还深入探讨了相应轨道的相对包含物结构。

附：英文原文

Title: Manifestly covariant worldline actions from coadjoint orbits. Part I. Generalities and vectorial descriptions

Author: Basile, Thomas, Joung, Euihun, Oh, TaeHwan

Issue&Volume: 2024-01-05

Abstract: We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian constraints which generate the coadjoint orbits of another, dual, Lie group. In case of (inhomogeneous) orthogonal groups, the dual groups are (centrally-extended inhomogeneous) symplectic groups. This defines a symplectic dual pair correspondence between the coadjoint orbits of the isometry group and those of the dual Lie group, whose quantum version is the reductive dual pair correspondence à la Howe. We show explicitly how various particle species arise from the classification of coadjoint orbits of Poincaré and (A)dS symmetry. In the Poincaré case, we recover the data of the Wigner classification, which includes continuous spin particles, (spinning) tachyons and null particles with vanishing momenta, besides the usual massive and massless spinning particles. In (A)dS case, our classification results are not only consistent with the pattern of the corresponding unitary irreducible representations observed in the literature, but also contain novel information. In dS, we find the presence of partially massless spinning particles, but continuous spin particles, spinning tachyons and null particles are absent. The AdS case shows the largest diversity of particle species. It has all particles species of Poincaré symmetry except for the null particle, but allows in addition various exotic entities such as one parameter extension of continuous particles and conformal particles living on the boundary of AdS. Notably, we also find a large class of particles living in “bitemporal” AdS space, including ones where mass and spin play an interchanged role. We also discuss the relative inclusion structure of the corresponding orbits.

DOI: 10.1007/JHEP01(2024)018

Source: https://link.springer.com/article/10.1007/JHEP01(2024)018