- #1
arroy_0205
- 129
- 0
It is well known that at times we do need explicit representations for the Dirac gamma matrices while doing calculations with fermions. Recently I found two different expressions for Majorana representation for the gamma matrices. In one paper, the form used is:
[tex]
\gamma_{0} = \left(
\begin{array}{cc}
0 & i\sigma_2\\
i\sigma_2 & 0
\end{array}
\right)
[/tex]
[tex]
\gamma_{1} = \left(
\begin{array}{cc}
\sigma_1 & 0\\
0 & \sigma_1
\end{array}
\right)
[/tex]
[tex]
\gamma_{2} = \left(
\begin{array}{cc}
0 & -i\sigma_2\\
i\sigma_2 & 0
\end{array}
\right)
[/tex]
[tex]
\gamma_{3} = \left(
\begin{array}{cc}
\sigma_3 & 0\\
0 & \sigma_3
\end{array}
\right)
[/tex]
[tex]
\gamma_{5} = \left(
\begin{array}{cc}
\sigma_2 & 0\\
0 & \sigma_2
\end{array}
\right)
[/tex]
However in wikipedia article on gamma matrices, the Majorana representations are diffenrent and all are complex matrices. See: http://en.wikipedia.org/wiki/Dirac_matrices#Majorana_basis
I am confused which is the actual representation of Majorana representation? Or are both representations valid Majorana representations? Note that in the rep. I wrote, the first four matrices are real matrices.
Also can anybody tell me how to write several matrices side-by-side in latex?
Thanks.
[tex]
\gamma_{0} = \left(
\begin{array}{cc}
0 & i\sigma_2\\
i\sigma_2 & 0
\end{array}
\right)
[/tex]
[tex]
\gamma_{1} = \left(
\begin{array}{cc}
\sigma_1 & 0\\
0 & \sigma_1
\end{array}
\right)
[/tex]
[tex]
\gamma_{2} = \left(
\begin{array}{cc}
0 & -i\sigma_2\\
i\sigma_2 & 0
\end{array}
\right)
[/tex]
[tex]
\gamma_{3} = \left(
\begin{array}{cc}
\sigma_3 & 0\\
0 & \sigma_3
\end{array}
\right)
[/tex]
[tex]
\gamma_{5} = \left(
\begin{array}{cc}
\sigma_2 & 0\\
0 & \sigma_2
\end{array}
\right)
[/tex]
However in wikipedia article on gamma matrices, the Majorana representations are diffenrent and all are complex matrices. See: http://en.wikipedia.org/wiki/Dirac_matrices#Majorana_basis
I am confused which is the actual representation of Majorana representation? Or are both representations valid Majorana representations? Note that in the rep. I wrote, the first four matrices are real matrices.
Also can anybody tell me how to write several matrices side-by-side in latex?
Thanks.
Last edited: