Name: Dimitry Fedorov (email_not_shown)
Date: 05/28/07-08:22:39 PM Z


Dear George,
unfortunately, I have not now a good reference to read about it. This is
fundamental property of Dirac matrixes, so, any arbitrary 4x4 matrix may be
decomposed as linear combination of Dirac matrixes Gamma=I, \gamma^5,
\gamma^{\mu},\gamma^5\gamma^{\mu}, \sigma^{\mu\nu}. Coefficients of this
decomposition may be determined by matrix trace operation (in addition
divided by 4). You can write your matrix M explicitly as 4x4 table in
Mathematica, after that you can write Dirac matrixes (for example in
standard representation) also as tables, after using usual 1/4*Tr[M.Gamma]
operation in Mathematica to define coefficients.

In FeynCalc these coefficients may be presented as numbers (before I and
\gamma^5 or components of four-vectors for other Dirac matrixes, all may be
expressed via known decomposition coefficients). You can define in FeynCalc
all scalar products values with these four-vectors using known coefficients
of matrix M decomposition.

Sincerely, Dimitry.

----- Original Message -----
From: George <noreply@feyncalc.org>
To: <feyncalc@feyncalc.org>
Sent: Monday, May 28, 2007 8:35 PM
Subject: Re: Multiplication of Dirac Gamma matrices by arbitrary matrix

> Dear Dimitry,
>
> Thank you very much for your advice....it is really helpfull.
> Could you also advise me how or /where to read how to decompose any
arbitrary matrix into gammas...or can FeynCalc do that?
>
> Thanks again
>



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