Image of the week: a root diagram and Dynkin diagrams

I’m not a mathematician, but Emi Yukawa and Kae Nemoto from the National Institution of Informatics in Japan certainly are. Their latest work in JPhysA studies squeezing — not physical squeezing, but a mathematical treatment of squeezing in a collective SU(2J+1) system consisting of spin-particles (J > 1/2). Our image of the week comes from visualising the roots of SU4 algebra and the following Dynkin diagrams.

 

(a) The root diagram of the su(4) algebra, (b) the Dynkin diagram of the the su(4) algebra, and (c) the four types of the unitary equivalence classes of the matrix representations of the su(2) subalgebras. In (c), the chosen simple roots and the omitted simple roots are indicated by the filled black circles and the open gray circles, respectively.

(a) The root diagram of the su(4) algebra, (b) the Dynkin diagram of the the su(4) algebra, and (c) the four types of the unitary equivalence classes of the matrix representations of the su(2) subalgebras. In (c), the chosen simple roots and the omitted simple roots are indicated by the filled black circles and the open gray circles, respectively. Copyright IOP Publishing, All Rights Reserved.

 

I must admit its a bit too much for me, but if you have a penchant for mathematics you can head over to JPhysA and read all about it here:

Read More: Classification of spin and multipolar squeezing


CC-BY logoThis work is licensed under a Creative Commons Attribution 3.0 Unported License

Image from Emi Yukawa and Kae Nemoto 2016 J. Phys. A: Math. Theor. 49 255301, Copyright IOP Publishing, All Rights Reserved.



Categories: Journal of Physics A: Mathematical and Theoretical

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