别名：Poincaré群
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Szekeres · source-snapshot-bc3404156f6e
已登记出处中的最早位置：§2.7 · zh-CN。
Woit · 2025-10-20
已登记出处中的最早位置：§40 · zh-CN。
来源短摘录与定位
§40 · zh-CN · machine_draft · machine-draft-not-reviewed
与非相对论情形一样，运动方程的解空间给出时空对称群的表示。这里的对称群是十维的Poincaré群(Poincaré group)，含四维时空平移子群和六维洛伦兹子群；后者包含空间旋转与混合时空坐标的推动变换。它在相对论波动方程解空间上的表示通常可约，而不可约表示对应基本粒子。本章讨论洛伦兹群，第41章讨论其表示，第42章再讨论Poincaré群及其表示。
§40 · en · machine_draft · machine-draft-not-reviewed
Just as in the non-relativistic case, the space of solutions to the equation of motion provides a representation of the group of space-time symmetries of the theory. This group will now be the Poincaré group, a ten dimensional group which includes a four dimensional subgroup of translations in space-time, and a six dimensional subgroup (the Lorentz group), which combines spatial rotations and “boosts” (transformations mixing spatial and time coordinates). The representation of the Poincaré group on the solutions to the relativistic wave equation will in general be reducible. Irreducible such representations will be the objects corresponding to elementary particles. This chapter will deal with the Lorentz group itself, chapter 41 with its representations, and chapter 42 will move on to the Poincaré group and its representations.
§42.1 · en · machine_draft · machine-draft-not-reviewed
Definition (Poincaré group)
The Poincaré group is the semi-direct product
with double cover
§42.1 · zh-CN · machine_draft · machine-draft-not-reviewed
定义（庞加莱群）
庞加莱群是半直积