Algebraic derivation of some theorems concerning contact structures on the 3-sphere
| Autor: | Dowker, J. S. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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$\pi$ 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 Schr\"odinger on Maxwell theory in an expanding universe. Comment: 13 pages. Amendment to text and 1 page explanatory Added Note regarding choice of expansion bases |
| Databáze: | arXiv |
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