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Openai/69174844-9774-8012-8b69-32262ca5e35a
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==== 1. 为什么要用“保持动量的不变子群”？ - 粒子的“内部自由度”必须在动量固定下定义（否则自旋状态随动量变化不一致） - 这个子群就是 Poincaré 群下保持参考动量不动的变换 ==== # 不同质量的粒子对应不同小群 - 有质量 → 静止系 → 小群 = SO(3) → 自旋 2s+1 - 无质量 → 沿动量参考系 → 小群 = ISO(2) → 仅 helicity ±s # 物理意义 - 电子、质子等有质量粒子 → 3 个自旋方向（1/2粒子 2 个投影） - 光子 → 只有两个偏振态 - 无质量粒子多余的自由度被规范或动力学约束去掉 我可以帮你画一张小群示意图： * 左边：有质量粒子静止系，SO(3) 旋转作用 * 右边：无质量粒子沿 z，ISO(2) 螺旋 + 平移（规掉） 这张图直观显示“为什么不同小群给出不同自由度”。 你希望我画吗？
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