Name: Dimitry Fedorov 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_at_HIDDEN-E-MAIL]>
To:
<[feyncalc_at_HIDDEN-E-MAIL]>
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
>