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"Now let us find Dirac Matrices [tex]\gamma^\mu[/tex] for four-dimensional Minkowski Space. It turns out that these matrices must be at least 4X4."

What is the proof of the above statement? I think (not sure) that it was once mentioned in class, that the above can be true only for a set of even dimensional matrices. Is that true? How?

And if yes, how do we know that the matrices can't be 2X2? Can someone show me a proof or guide me in the right direction.

Thanks.