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  Good pedagogical introduction to Young-tableaux and weight diagrams?

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I am looking for a short pedagogical introduction to Young-tableaux and weight diagrams and the relationship between them, which contains many detailled and worked out examples of how these methods are applied in physics, such as in the context of the standard model and beyond for example.

I am rather looking for a resource that is dedicated specifically to this topics, which I can easily print out, conversely to a heavy general group-theory textbook.

asked Aug 7, 2015 in Resources and References by anonymous [ no revision ]

1 Answer

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A classic reference is Richard Slansky's "Group Theory for Unified Model Building" available at http://cds.cern.ch/record/134739/files/198109187.pdf.

I'm sure you're aware of Howard Georgi's book "Lie Algebras in Particle Physics". It has a coverage of all the topics you mention. Note that Young Tableaus are usually discussed in the book for SU(n) groups. Rules for SO(n) groups are of little or no use to particle physicists I suppose, but they are useful if you study string theory or supergravity. For such cases, there's a paper by Mark Fischler (I think it is here: http://scitation.aip.org/content/aip/journal/jmp/22/4/10.1063/1.524969 but I could be wrong). There are also some useful notes by Peter van Nieuwenhuizen, available at https://sites.google.com/site/vannieuwenhuizengrouptheory/home.

Note that there is some group and representation theory you absolutely need to know before you will find their references in standard model or particle physics literature useful. The short introductions usually tell you obvious things (what is a group, what is a representation?) and you do need to work out several examples yourself before you can get a hang of things. If your interest is not in formal group theory or formal theoretical physics but more applied/phenomenological stuff, then you should at least know most of Georgi's book well.

There is a recent book by Ken Barnes (http://www.amazon.com/Standard-Particle-Physics-Cosmology-Gravitation/dp/1420078747/ref=sr_1_1?s=books&ie=UTF8&qid=1439157644&sr=1-1&keywords=standard+model+group+theory) but I haven't seen it myself, so I can't comment on how useful it'll be.

The bottom line is that if you're primarily interested in tableaux and weight diagrams, the Google sites link above may be most appropriate.

answered Aug 9, 2015 by leastaction (425 points) [ revision history ]
edited Aug 9, 2015 by leastaction

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