Classification of AllC-Noninvariant Electromagnetic Interactions and the Possible Existence of a Charged, butC=1, Particle

Assuming that the strong interaction $H_{\mathrm{st}}$ is invariant under the particle-antiparticle conjugation $C$, it is shown that all possible $C$-noninvariant electromagnetic interactions $H_{\gamma }$ can be classified according to the anticommutator between $C$ and the charge operator $Q$ into two types: (1) $\{C, Q\}=0\mathrm{}$ and (2) $\{C, Q\}\ne 0$. Discussions of the first type $C$-noninvariant minimal electromagnetic interaction have already been given in a previous paper. If $\{C, Q\}\ne 0$, then the operator $C$ must be different from what is normally called the "charge-conjugation operator" $C_{\gamma }$ which, by definition, changes any state of charge $Q$ to that of $-Q$. Thus, $\{C_{\gamma }, Q\}=0\mathrm{}$ and $C\ne C_{\gamma }$. As a consequence, there must exist, at least, a charged particle $a^{+}$ which is an eigenstate of $C$; its eigenvalue can always be chosen to be +1. Furthermore, in the framework of a Lorentz-invariant local-field theory, $H_{\mathrm{st}}$ and $H_{\gamma }$ are invariant under $C_{\gamma }\mathrm{PT}$, but not $\mathrm{CPT}$. The $C_{\gamma }\mathrm{PT}$ invariance requires the existence of another charged particle $a^{-}$ which has the same mass as $a^{+}$ but the opposite charge. The $a^{-}$ is also an eigenstate of $C$. The existence of such $a^{\pm }$ particles necessitates not only the $C$ nonconservation of $H_{\gamma }$, but also the $T$ noninvariance of $H_{\mathrm{st}}$. The general algebraic relations between $H_{\mathrm{st}}$, $H_{\gamma }$, and these symmetry operators are studied, and the properties of the particles $a^{\pm }$ are discussed. An explicit spin-½ model of $a^{\pm }$ based on the...