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.