In the Quantum electrodynamics book (look at the problem) its authors Lifshitz and Berestetskei claim that operator of charge conjugation ˆC=−α2 in Majorana basis transforms as ˆCM=α2. Here (they started from the standart (Dirac) representation of the gamma-matrices) α2=(0σyσy0),β=(100−1), ˆCM=ˆU+ˆCˆU,ˆU=1√2(α2+β)=1√2(1σyσy−1)=ˆU+. I tried to get their result, but I only got ˆCM=12(1σyσy−1)(0σyσy0)(1σyσy−1)=(100−1), because σ2y=1.
Where is the mistake?
An edit.
I found the mistake. I used the wrong definition of transformation of charge conjugation operator under unitary spinor transformation. The correct one is ˆC′=ˆUˆCˆUT.
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