Difference between revisions of "Yang-Baxter equation"

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(Created page with "<div class="floatright" style="text-align: center"> center|class=shadow|300px </div> In physics, the Yang–Baxter equation (or star–trian...")
 
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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, {\displaystyle R}R is the scattering matrix and if it satisfies the Yang–Baxter equation then the system is integrable. The Yang–Baxter equation also shows up when discussing knot theory and the braid groups where {\displaystyle R}R corresponds to swapping two strands. Since one can swap three strands two different ways, the Yang–Baxter equation enforces that both paths are the same.
In one dimensional quantum systems, $${R}$$ is the scattering matrix and if it satisfies the Yang–Baxter equation then the system is integrable. The Yang–Baxter 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 Yang–Baxter 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: ==
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