Date: Thu, 09 Jan 2003
From: Giovanni Cicuta
Dear Predrag,
I am happy your book will appear. I gave a very quick reading to the parts
of
http://www.cns.gatech.edu/GroupTheory/chapters/GroupTheory.pdf
which are closer to my interests. A few
insignificant comments and references (mine) are here attached.
Yours, Giovanni
Color decomposition and color basis.
Several papers on QCD by Bern, Dixon, Kosower and others discuss those
decompositions . Your old paper on gauge sets,
Cvitanovic, Lawres, Scharbach, Nucl.Phys B186, (1981) 165 ,
is occasionally quoted.
A more recent paper is :
\bibitem{Duca:2000} V.~Del~Duca, L.~J. Dixon and F.~Maltoni,
% Vittorio Del Duca, Lance J. Dixon, Fabio Maltoni .
``New color decompositions for gauge amplitudes
at tree and loop level,''
% SLAC-PUB-8294, DFTT-53-99, Oct 1999. 17pp.
{\em Nucl. Phys. B \bf 571}, 51 (2000); %51-70
\arXiv{hep-ph/9910563}.
Long ago in the paper GAUGE SETS AND 1/N EXPANSION, By E. Ciapessoni, G.M.
Cicuta , Published in Nucl.Phys.B219 (1983) 513-523,
I found that your diagrammatic methods are very effective to find useful
tensor basis to espress sets of gauge invariant amplitudes (as I wrote in
the acknowledgment, you corrected a mistake in the first draft of the
paper). I think that the works on the subject in the following 20 years
were not very new and they did not use the most effective tools.
Maybe it would be good to have a remark in your book to the usefulness of
the gauge invariant sets described in your paper (1981), their relevance
in perturbative QCD, and the usefulness of diagrammatic methods to this
problem.
References
I have no suggestion for references that you should add in your book. As
to references that you may add, there are very many. But let me worn you :
an author not quoted is unhappy, but he is more unhappy if very many
papers similar to his own are quoted. Then as you add references, it is
likely that more people will be unhappy.
I have a few old papers where I did use your diagrammatic methods ,
occasionally I did a very a straightforward elaboration and I often
stressed the usefulness of diagrammatic notation and tools.
\bibitem{Cicuta:1982} G.M. Cicuta, %(Milan U. & INFN, Milan).
``Topological expansion for SO(n) and SP(2n) gauge theories,''
{\em Lett. Nuovo Cim. \bf 35}, 87 (1982).
Here I describe the large-n expansion for gauge theories
with SO(n) or Sp(n) groups. The problem had previously been discussed in a
more limited way by Canning, Phys.Rev.D12 (1975), 2506. Your diagrammatic
techniques are used. The replacement n to -n for gauge invariant
quantities of the SO(n) and SP(n) models is noted, as well as your
previous work with Kennedy.
- HIGH-ENERGY LIMIT AND INTERNAL SYMMETRIES. By G.M. Cicuta, D. Gerundino
(Milan U.). Published in Phys.Rev.D29:1258-1266,1984
Most of the new work in this paper is the evaluation of group factors in
SU(N) for classes of relevant Feynman graphs. One can perform series
summations after decomposing contributions with different quantum numbers
(actually contributions belonging to different representations of the
group). This is done using projectors. We interacted during the work and
you made contributions. In the end, instead of an acknowledgment you
preferred a sentence, which appear as reference n.11.
- DIAGONALIZATION OF A COLORING PROBLEM (ON A STRIP).
By G.M. Cicuta, A. Pavone Published in J.Phys.A22:4921,1989
Here I considered a problem exactly solved by Baxter : evaluating the
number of ways of proper coloring (with 3 colors) the bonds of a lattice
made by regular exagons. You may view this lattice as made by rectangular
bricks, the way brick walls are made. And consider a strip of the brick
wall, the projectors of SU(2), here I am using Penrose and your results.
The transfer matrix corresponding to a strip of finite width provides an
approximation to the exact Baxter result, obtained by a completely
different approach.