Majorana representation of Gamma matrices.

[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:
<br /> \gamma_{0} = \left(<br /> \begin{array}{cc}<br /> 0 &amp; i\sigma_2\\<br /> i\sigma_2 &amp; 0<br /> \end{array}<br /> \right)<br />
<br /> \gamma_{1} = \left(<br /> \begin{array}{cc}<br /> \sigma_1 &amp; 0\\<br /> 0 &amp; \sigma_1<br /> \end{array}<br /> \right)<br />
<br /> \gamma_{2} = \left(<br /> \begin{array}{cc}<br /> 0 &amp; -i\sigma_2\\<br /> i\sigma_2 &amp; 0<br /> \end{array}<br /> \right)<br />
<br /> \gamma_{3} = \left(<br /> \begin{array}{cc}<br /> \sigma_3 &amp; 0\\<br /> 0 &amp; \sigma_3<br /> \end{array}<br /> \right)<br />
<br /> \gamma_{5} = \left(<br /> \begin{array}{cc}<br /> \sigma_2 &amp; 0\\<br /> 0 &amp; \sigma_2<br /> \end{array}<br /> \right)<br />
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.

 

[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?

 

[mjsd]

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

 

[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.