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- W3010994403 abstract "The aim of this paper will be to demonstrate how many of the most important properties ofSU(3) may be derived simply and directly using only the elements of group theory. (As I use thephrase, “the elements of group theory” consist of the contents of WIGNER’s book [1]. However, wewill need only a small subset of this.)In the first part of the paper I will show how we can deduce many useful facts about theirreducible representations of SU(3) by simple tensorial methods. In particular, I will develop twoalgorithms, one for the isospin-hypercharge content of an irreducible representation, and one forthe Clebsch-Gordan series, that I think are simpler and more efficient than most presented in theliterature. In addition, they are very easy to derive. This is an important practical matter. Thereare many splendid methods of calculation whose use requires either an excellent memory or a copy ofHamermesh∗; without these, all is lost. I hope that once you have seen me derive these algorithms,you will be able to derive them again, when the need to apply them occurs, on the back of anenvelope, if necessary.In the second part of the paper I will show how these methods can be used to show that the objectswe have been manipulating are in fact a complete set of inequivalent irreducible representations. Thisis practice before theory, the reverse of the usual mathematical order, but nevertheless the mostexpedient way to do things here.At the end I will make some remarks about the calculation of invariant couplings (Clebsch-Gordancoefficients). What I have to say will be neither very general nor (I am afraid) very impressive, butit fits in with the tensorial methods used in the other two parts. Perhaps one of you will be cleverenough to figure out how to make the methods I will present here more general and more powerful.Finally, I should apologize for the fact that this paper will contain so much mathematics and solittle physics. This is not because I believe this is the way SU(3) should be taught, but only becausethe physics has already been covered in Prof. Lipkin’s† paper.1" @default.
- W3010994403 created "2020-03-23" @default.
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- W3010994403 date "2019-02-19" @default.
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- W3010994403 title "Fun with SU(3)" @default.
- W3010994403 hasPublicationYear "2019" @default.
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