Sunday, 17 June 2018

dirac matrices - Are Lifshitz and Berestetskii right in this case?


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=(1001), ˆCM=ˆU+ˆCˆU,ˆU=12(α2+β)=12(1σyσy1)=ˆU+. I tried to get their result, but I only got ˆCM=12(1σyσy1)(0σyσy0)(1σyσy1)=(1001), 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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