Name: Frederik Orellana Date: 02/13/02-10:43:10 AM Z

Hello there.

To work with different SU groups, the FeynCalc SU(N) functions SUNF, SUND,
SUNDelta and SUNT would have to be modified. As it is now, SUNTrace and
SUNSimplify return results in terms of SUNN (or CA, CF which depend on
SUNN) and SUNN is the unique dimension (or number of colors). Alternatively
one could modify these functions to take an option, say “SUNN->m” and have
UNTrace and SUNSimplify check the dimension of things and return results in
terms of m instead of SUNN where appropiate.

This should not be too much of a work, however it’s also not done in a
couple of hours. I’m willing to do it when I find time if there are others
needing this feature. Otherwise, you are of course welcome to give it a try
yourself and send me the modified files, which I could then incorporate
into the distribution.

Best wishes,

Frederik

At 18:40 11-02-2002 +0000, you wrote:

>Is it possible, within FeynCalc, to work with expressions containing
>structure constants from SU(N) groups with different values of N ?
>
>For example, contractions of objects with SU(N) indices already yield
>answers which depend on N in the desired way, such as:
>
> SUNSimplify[SUNF[a,b,c] SUNF[a,b,d],SUNNToCACF -> False]
>
>which evaluates to
>
> N \delta_{c d}
>
>as expected.
>
>If however, I were to have a more complicated product of four
>structure constants; two from SU(N) (contracted together) and two
>from SU(M) (contracted together); then I would like to be able to
>simplify the whole expression and obtain an answer like
>
> N M \delta_{c d} \delta_{g h}.
>
>Is it possible to attach particular dimensions M and N to different
>structure constants?
>
>Many thanks,
>
>Christopher
>
>P.S. I snooped around in the code FeynCalc.m a bit to see if I
>could spot a solution in there, and I wondered if SUNF2[…] (as
>opposed to SUNF[…]) might help me out, however SUNSimplify[…]
>does not seem to simplify expressions composed of SUN2[…] objects,
>so I guess I should leave them well alone …
>
>——————————————————
>Christopher Lester Tel: +44 1223 766300
>Cavendish Lab., Madingley Road, Cambridge, CB3 0HE, UK