Three-Cocycle in Mathematics and Physics
- 21 January 1985
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 54 (3), 159-162
- https://doi.org/10.1103/physrevlett.54.159
Abstract
It is shown that the three-cocycle arises when a representation of a transformation group is nonassociative, so that the Jacobi identity fails. A physical setting is given: When the translation group in the presence of a magnetic monopole is represented by gauge-invariant operators, a (trivial) three-cocycle occurs. Insisting that finite translations be associative leads to Dirac's monopole quantization condition. Attention is called to the possible relevance of three-cocycles in the quark model's U(6) ⊗ U(6) algebra.Keywords
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