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Hi,

I have developed a Mathematica program that computes the traces of

gamma-matrices, simplifies sums of delta-functions (Einstein summation

convention), and evaluates certain types of Feynman integrals, namely the

ones in Itzykson and Zuber "QFT", pp. 419-422. I took much trouble to

simplify the intermediate expressions in a useful, controlled and general

way, this is roughly 80% of the code.

Though the code has been debugged, I do not get the results in I-Z;

perhaps they are incorrect. An indication of this is Eq. (8-119) in that

book. It is not manifestly symmetric in rho and sigma, and in fact the trace

of the gamma matrices is not symmetric in rho and sigma at all. Theory says

that \Gamma in (8.115) is symmetric in rho and sigma, but that's only after

the integration is performed. I do not get their result whether or not I

symmetrize (8-119). The situation in I-Z is delicate anyway, as analysis

shows that one of the integrals on p. 421 is divergent, so there is some

question of what an "exact" calculation should give.

I'd be interested in hearing from others who have attempted the

calculations in I-Z, and suggest this as a rather stringent test case.

(Incidentally, it is outrageous of I-Z to have included such a brutish

calculation in what is supposed to be a textbook, without even indicating

that the calculations were computer-aided.)

I have two files, a run file and a code file. Five or six pages of

analysis are also available (power-counting to keep track of divergences,

organization of the calculations).

Yours truly,

Alan Mason

PS. It would be good to have software to automatically evaluate integrals

like (5.23) in Abrikosov et al. "Methods of QFT in Stat. Phys." See paper by

Belyakov (Sov. Phys. JETP, Vol. 13, No. 4) . The problem is to automate the

handling of the domains of integration; perhaps this is too difficult though

it can be done by hand in this special case. Has anyone obtained Belyakov's

results using Mathematica?

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