In the "QFT Nutshell" by A. Zee, it is stated that

The Majorana equation is $$i\not\partial\psi=m\psi_c$$ where $\psi_c$ is the charge conjugated spinor $\psi_c = \left(C\gamma^0\right)\psi^*$. As $\psi_c$ is right handed if $\psi$ is left handed, the Majorana equation, unlike the Dirac equation, preserves handedness.

I have completely no idea what the author means when he says "the equation preserves handedness".

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    $\begingroup$ Do you appreciate handedness (chirality) and how the massive Dirac's equation violates it? (connects left- to right-handers). $\endgroup$ – Cosmas Zachos Aug 6 at 0:43
  • $\begingroup$ I think understand the chirality. It is how the spin of the particle relates to its direction of motion. I am not really sure how the massive Dirac's equation violates the chirality. But if I were to guess, I would say that by looking at the Dirac's Lagrangian, the mass terms connect the left handed spinor to the right handed spinor. Is that the correct way to see? $\endgroup$ – TangBear Aug 6 at 9:17
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    $\begingroup$ You are close, but you are confusing helicity with chirality, which makes all the difference: for Tony, "handedness" is chirality! Go to a world without right-chiral particles. Note that you cannot write a massive Dirac equation there, but you can a Majorana equation. $\endgroup$ – Cosmas Zachos Aug 6 at 13:34
  • $\begingroup$ I think I understand now. Thank you very much! $\endgroup$ – TangBear Aug 6 at 15:37

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