三维李群上的左不变Rarita-Schwinger场
Left-invariant Rarita-Schwinger fields on 3-dimensional Lie groups
AI总结：
本文分类了带左不变黎曼度量的二维、三维李群上的左不变Rarita-Schwinger场，将对应方程简化为代数系统，得出二维非平凡例仅在平坦阿贝尔情形、三维额外例在带特殊左不变度量的SU(2)上且场空间复维数为2的结论。
AI中文摘要：
我们对带有左不变黎曼度量的二维和三维李群上的左不变Rarita-Schwinger场进行分类，将左不变Rarita-Schwinger方程简化为关联度量李代数上的代数系统。结果表明，二维时非平凡例子仅出现在平坦阿贝尔情形；三维时除平坦阿贝尔情形外，唯一非平凡例子出现在配备特殊左不变度量的SU(2)上，此时左不变Rarita-Schwinger场空间的复维数为2，该度量是S³上的Berger度量。
英文摘要：
We classify left-invariant Rarita-Schwinger fields on 2- and 3-dimensional Lie groups with left-invariant Riemannian metrics. The left-invariant Rarita-Schwinger equation is reduced to an algebraic system on the associated metric Lie algebra. We show that, in dimension 2, non-trivial examples occur only in the flat abelian case. In dimension 3, apart from the flat abelian case, the only non-trivial examples occur on SU(2) equipped with a special left-invariant metric, for which the space of left-invariant Rarita-Schwinger fields has complex dimension 2. This metric is a Berger metric on $S^3$.
