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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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