关于3维球面上切触结构若干定理的代数推导
Algebraic derivation of some theorems concerning contact structures on the 3-sphere
AI总结：
该研究利用角动量理论代数推导3维球面上切触结构的两个相关定理，以旋量超球谐函数为基，证明奇旋度本征场消失性，推导常模旋度本征场与Hopf场成比例的结论，并提及Schrödinger早期相关工作的价值。
摘要：
本文利用角动量理论得到了两个涉及3维球面上旋度本征场的定理。研究表明，旋量超球谐函数构成了一种显式且便捷的基。文中特别回顾了自旋为1的矢量微积分。给出了“奇”本征场消失性的简单证明，并将其与费米子旋量在2π旋转下的符号变化相关联。还快速推导了如下定理：具有常模的旋度本征场必定与基本本征场（Hopf场）成比例。文中还提请关注Schrödinger早期关于膨胀宇宙中Maxwell理论工作的相关性。
英文摘要：
Two theorems involving curl eigenfields on the 3--sphere are obtained using angular momentum theory. Spinor hyperspherical harmonics are shown to form an explicit, convenient basis. In particular, a spin--one vector calculus is reviewed. An easy proof of the vanishing of `odd' eigenfields is given and related to the sign change of fermionic spinors under 2$π$ rotations. The theorem that curl eigenfields with constant norm have to be proportional to a fundamental eigenfield (Hopf field) is also rapidly obtained. Attention is drawn to the relevance of early work of Schrödinger on Maxwell theory in an expanding universe.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
