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I know C parity as an operator : $$ C\psi=\pm\psi $$ has two eigenvalues like parity operator P. But what I wonder is, i.e, is it true to say for a negative charged particle has (-) eigenvalue? If not what is the way to relate them?

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    $\begingroup$ Have you read the article you link? "so only truly neutral systems – those where all quantum charges and the magnetic moment are zero – are eigenstates of charge parity" $\endgroup$ – ACuriousMind Apr 17 '15 at 16:35
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The charge parity operator $\newcommand{\C}{\mathcal C}\C$ takes each particle to its antiparticle, which has opposite charge. As such, its eigenstates are those states that remain the same if you change all particles for their antiparticles. This can happen, for example,

  • in a state that contains two particles which are each other's antiparticle, such as one electron and one positron, in which case switching the electron to a positron and the positron to an electron does not change the total particle content of the state, or
  • in a state that only contains particles that are their own antiparticles, like bosons or Majorana fermions.

A state that contains a single electron, on the other hand, will not be an eigenstate of $\C$. Instead, it is an eigenstate of the total charge operator $\mathcal Q$, for which its eigenstate is indeed $-1$.

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