# Majorana representation of Gamma matrices.

1. Jul 13, 2008

### arroy_0205

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:
$$\gamma_{0} = \left( \begin{array}{cc} 0 & i\sigma_2\\ i\sigma_2 & 0 \end{array} \right)$$
$$\gamma_{1} = \left( \begin{array}{cc} \sigma_1 & 0\\ 0 & \sigma_1 \end{array} \right)$$
$$\gamma_{2} = \left( \begin{array}{cc} 0 & -i\sigma_2\\ i\sigma_2 & 0 \end{array} \right)$$
$$\gamma_{3} = \left( \begin{array}{cc} \sigma_3 & 0\\ 0 & \sigma_3 \end{array} \right)$$
$$\gamma_{5} = \left( \begin{array}{cc} \sigma_2 & 0\\ 0 & \sigma_2 \end{array} \right)$$
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: Jul 14, 2008
2. Jul 14, 2008

### arroy_0205

Is there any definite rule to obtain gamma matrix representations? Or can I use my own representations if I find the matrices satisfy the anticommutation relations? Is there any limit on the number of possible representations of gamma matrices in a given dimension?

3. Jul 21, 2008

### mjsd

gamma matrices are only defined up to similarity transformations; which representation or basis you wish to use is up to you.

4. Jul 21, 2008

### Haelfix

They're also amongst the leading causes of stress disorders amongst physicists.

The number of times a factor of i, or -1 from a mismatch of conventions with them, has bungled a calculation at this point is a matter of historical importance.