birdtracks - who to cite?

 
If it was done first by a physicist, in mathematics the custom is to cite the first famous mathematician who redid it later. In physics it used to be one cited the person who did it first, regardless of the trade union affiliation (can you name the person who invented general relativity second?), but with the advent of string theory these quaint old customs might have fallen by the wayside.
The history of birdtracks is given in the book, sect 4.6. Please email me info about any important references I might have missed. What follows is mostly for your amusement.
 
from Rob Pisarski to Predrag Cvitanovic, Apr 20, 2009
 
Recently I did a calculation in thermal field theory. I and Yoshimasa Hidaka wrote a little section on birdtracks which you might find amusing.
In the end its very simple, although the whole thing about the difference between the normalization of the diagonal and off-diagonal generators confused us terribly. I started doing the computation in the Cartan basis, which is a horror. It confused us, and we did not find a discussion of such in your book. Then Yoshimasa came up with stuff which eventually became what we call the 't Hooft basis.
You will probably be annoyed by our describing things as the 't Hooft basis. It is a suggestion, nothing more.
Mainly I just wanted to make sure that you didn't barf about the name. Thing is, if you name something after somebody already famous, more likely to stick. You know there were four people on the paper that first introduced Landau gauge? Computing the electron wave function renormalization. Only Landau's name stuck.
We would appreciate any comments from you, as the Master Of Birdtracks.
 
 
from Predrag Cvitanovic to Rob Pisarski, Apr 22, 2009
 
Already famous? I have heard of Landau, but who is this guy 't Hooft? Maybe the smart guy from my PhD year whose first name was pronounced HaHa with a boiled potato stuck down your throat? I could never figure out the spelling - Dutch can be hard on foreigners, specially on us Danes whose language is so beautiful. Whatever became of him, anyway? Is he on Facebook?
Seriously, I'm a fan. I tried (and failed) many times to draw his portrait on the cover of FieldTheory, Feynman got on the cover only as my second choice. For U(N) the `birdtrack' double-line notation notation was introduced by 't Hooft in 1974, so you are absolutely right to credit him. U(N) is all he needed to get the leading term in the 1/N expansion. Crediting 't Hooft for indexing adjoint rep by 2 defining indices is not fair to dead white men - the practice is much older than any of us. For example, commutators of SO(4) that the general relativists use have double indices, see book sect 4.6.
Projection operators for SU(N) seems to have been first introduced for the purpose they are used in your paper, exact calculation of group-theoretical weights, by some @?$*! (rhymes with Sonofwhich) in his 1976 paper. They are not in 't Hooft original 1974 paper. If you find some earlier reference, please let me know, so I can correct that in the web version of birdtracks.eu.
What I would do is read `Chap 1 - Introduction' to the book, where the reason why people who compute more complicated group theory weights than the quadratic casimir eventually abandon the Cartan basis is explained. I refer to the basis you use as the “invariant tensor basis,” or, if you like to attach difficult-to-spell names to such things, call it after the person(s) who introduced it first. I know of no literature which would justify calling it a “'t Hooft basis.”
Thanks for being so kind to `birdtracks' in your article. And, quoting Oscar Wilde (perhaps) “You can write anything you want about me, just spell my name right:” Cvitanovi\'c.
Master Birdcatcher
Other frequently asked questions