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i have a question , how did Dirac derive the existence of antimmater from his equation ??

$$i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0$$

and why for the Majorana equation predicts the existence of massive particles which are their own anti- particles ?

the majorana equation is real valued only ? $$ i \, {\partial\!\!\!\big /} \psi - m\, \psi_c = 0~ $$

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Dirac did not originally predict antimatter. He thought that the positive charged particle should be the proton. That the theory forced it to have the same mass of the electron was a seen as a failure of his equation. It was only after the experimental discovery of antimatter that the equation was understood to be correctly describing the positron.

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