关于无质量玻色子自旋与轨道角动量存在性的四个不可能定理
Four no-go theorems on the existence of spin and orbital angular momentum of massless bosons
AI总结：
本文证明无质量玻色子的总角动量通常不能分解为自旋与轨道角动量，并将该不可能结果推广到非内部对称性及非 SO(3) 对称性情形。
摘要：
在过去几十年中，人们对所谓的光的轨道角动量（OAM）表现出极大兴趣，这主要是由其广泛的应用所推动。然而，将光子等无质量粒子的角动量分解为自旋（SAM）部分和轨道角动量部分存在根本性的理论问题。尽管有质量粒子的角动量可以自然地分解为 Wigner SAM 和 OAM，但人们针对光子提出了众多分解方案，对于哪一种正确尚无共识。此外，已有研究表明，大多数被提出的 SAM 和 OAM 算符并不满足角动量算符的定义对易关系，因此不是合法的分解。在这里，我们证明，通常不可能将光子和引力子等无质量玻色子的总角动量算符分解为自旋部分和轨道部分。我们证明了这一结果的两个进一步推广，表明即使在以下情形下也不存在 SAM-OAM 分解：（1）SAM 算符生成非内部对称性，或（2）允许 SAM 和 OAM 算符生成非 SO(3) 对称性。
英文摘要：
The past decades have seen substantial interest in the so-called orbital angular momentum (OAM) of light, driven largely by its diverse range of applications. However, there are fundamental theoretical issues with decomposing the angular momentum of massless particles, such as photons, into spin (SAM) and orbital angular momentum parts. While the angular momentum of massive particles has a natural splitting into the Wigner SAM and OAM, there are numerous proposed splittings for photons and no consensus about which is correct. Moreover, it has been shown that most of the proposed SAM and OAM operators do not satisfy the defining commutation relations of angular momentum operators and are thus not legitimate splittings. Here, we prove that it is generally impossible to split the total angular momentum operator of massless bosons, such as photons and gravitons, into spin and orbital parts. We prove two further generalizations of this result, showing that there are no SAM-OAM splittings even if (1) the SAM operator generates non-internal symmetries or (2) if one allows the SAM and OAM operators to generate non-SO(3) symmetries.
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