Thanks for the thread. Interesting to hear that you are sold on this, Predrag.
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Replying to @stevenstrogatz @chaaosbook and
Sold on it? He practically wrote the book! And the book is here: http://birdtracks.eu/version9.0/GroupTheory.pdf …
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Replying to @johncarlosbaez @chaaosbook and
I wasn’t talking about bird tracks! I know Predrag wrote the book – I have it, and love it! I was talking about the newly proposed diagrammatic approach to vector calculus (The topic of Predrag’s thread; I asked him about it because I know he likes diagrammatic methods.)
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Replying to @stevenstrogatz @chaaosbook and
The diagrammatic methods for vector calculus and the diagrammatic methods for group representation theory are two aspects of the same game. Penrose invented these methods for tensor calculus, which combines vector calculus and group rep theory. So Predrag should like both.
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Replying to @johncarlosbaez @chaaosbook and
Ok, thanks. I had not appreciated that the vector calculus diagrammatic methods were essentially the same thing as the methods for group theory.
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Replying to @stevenstrogatz @chaaosbook and
Yeah, the cool thing is that all the usual operations in 3d vector calculus are covariant under 3d rotations, so they're all about "things you can do with representations of SO(3)". The all-important Levi-Civita symbol epsilon_{ijk} is the star of the show here.
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Replying to @johncarlosbaez @stevenstrogatz and
For other groups would it be replaced by the "stucture constants" of the respective Lie algebra?
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Replying to @Quantensalat @johncarlosbaez and
The structure constants are one of the types of objects that show up, but not the only one. The objects that show up are sometimes called "invariant tensors" or invariant symbols. 1/
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Replying to @duetosymmetry @Quantensalat and
holy crap i can actually say 'i wrote a relevant paper on this' https://arxiv.org/pdf/1806.04332.pdf …
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Replying to @InertialObservr @Quantensalat and
Aha! I guess the representation-theorist would say you are using the "induced representation" of a subgroup to lift up to the whole group?
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Replying to @duetosymmetry @Quantensalat and
yea! that's pretty much the idea.
4:42 PM - 9 Dec 2019
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