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Yang-Baxter equation: Difference between revisions
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(Created page with "<div class="floatright" style="text-align: center"> center|class=shadow|300px </div> In physics, the YangâBaxter equation (or starâtrian...") Â |
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:$${ ({\check {R}}\otimes \mathbf {1} )(\mathbf {1} \otimes {\check {R}})({\check {R}}\otimes \mathbf {1} )=(\mathbf {1} \otimes {\check {R}})({\check {R}}\otimes \mathbf {1} )(\mathbf {1} \otimes {\check {R}})}$$ | :$${ ({\check {R}}\otimes \mathbf {1} )(\mathbf {1} \otimes {\check {R}})({\check {R}}\otimes \mathbf {1} )=(\mathbf {1} \otimes {\check {R}})({\check {R}}\otimes \mathbf {1} )(\mathbf {1} \otimes {\check {R}})}$$ | ||
In one dimensional quantum systems, { | In one dimensional quantum systems, $${R}$$ is the scattering matrix and if it satisfies the YangâBaxter equation then the system is integrable. The YangâBaxter equation also shows up when discussing knot theory and the braid groups where $${R}$$ corresponds to swapping two strands. Since one can swap three strands two different ways, the YangâBaxter equation enforces that both paths are the same. | ||
== Resources: == | == Resources: == | ||
*[https://en.wikipedia.org/wiki/Yang%E2%80%93Baxter_equation Yang-Baxter equation] | *[https://en.wikipedia.org/wiki/Yang%E2%80%93Baxter_equation Yang-Baxter equation] | ||
== Discussion: == | == Discussion: == | ||