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"A bunch of cool complex analysis stuff popped up and solved my problem" is about as honest as it gets. But physicists do this from more or less their first differential equation: using $e^{i \omega t}$ to track both solutions via the cool-ness of complex analysis. There's no a priori or manifestly physics-based reason to do it that way. In the "original" ...


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Mathematically, the R-matrix is an (invertible) element of a quasi-triangular Hopf algebra. The R-matrix there is what "controls" the failure of the cocommutativity of your Hopf-algebra, and the Yang-Baxter equation is a consequence of all that. You can interprete it as a "braid-like" equation. See the wiki-pages on these subjects for more precisions. In ...



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