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

Abstract

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 ${H}_{\ensuremath{\gamma}}$ can be classified according to the anticommutator between $C$ and the charge $Q$ into two types: (1) ${C, Q}=0$ and (2) ${C, Q}\ensuremath{\ne}0$. Discussions of the first type $C$-noninvariant minimal electromagnetic interaction have already been given in a previous paper. If ${C, Q}\ensuremath{\ne}0$, then the $C$ must be different from what is normally called the charge-conjugation operator ${C}_{\ensuremath{\gamma}}$ which, by definition, changes any state of charge $Q$ to that of $\ensuremath{-}Q$. Thus, ${{C}_{\ensuremath{\gamma}}, Q}=0$ and $C\ensuremath{\ne}{C}_{\ensuremath{\gamma}}$. 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 ${H}_{\ensuremath{\gamma}}$ are invariant under ${C}_{\ensuremath{\gamma}}\mathrm{PT}$, but not $\mathrm{CPT}$. The ${C}_{\ensuremath{\gamma}}\mathrm{PT}$ invariance requires the existence of another charged particle ${a}^{\ensuremath{-}}$ which has the same mass as ${a}^{+}$ but the opposite charge. The ${a}^{\ensuremath{-}}$ is also an eigenstate of $C$. The existence of such ${a}^{\ifmmode\pm\else\textpm\fi{}}$ particles necessitates not only the $C$ nonconservation of ${H}_{\ensuremath{\gamma}}$, but also the $T$ noninvariance of ${H}_{\mathrm{st}}$. The general algebraic relations between ${H}_{\mathrm{st}}$, ${H}_{\ensuremath{\gamma}}$, and these symmetry operators are studied, and the properties of the particles ${a}^{\ifmmode\pm\else\textpm\fi{}}$ are discussed. An explicit spin-\textonehalf{} model of ${a}^{\ifmmode\pm\else\textpm\fi{}}$ based on the principle of minimal electromagnetic interaction is given. A possible unifying view connecting the present $C$, $T$ noninvariance with the well-known $C$, $P$ nonconservation of the weak interaction is discussed.