Consider a positive-energy solution with charge . The equivalent Klein-Gordon equation satisfied by the positive-energy solution is

The negative energy solution satisfies

(4.78) |

Taking the complex conjugate of the negative energy equation gives

Comparing equation 4.77 with equation 4.79 shows

(4.80) |

Thus is the charge conjugate solution and represents the charge conjugate state of . Similarly, is the charge conjugate state of . If we (arbitrarily) call the particle described by ``the particle'', then we call the particle described by the antiparticle. For example, if we call the meson the particle, then the meson is the antiparticle. The undesirable negative-energy solutions have now been interpreted as antiparticles.

Neutral particles fit into this picture too, in that the charge-conjugate state is the state itself. In other words, neutral particles are their own antiparticles. Let and so that we can write

(4.81) |

where is a proportionality constant which has to be real. can be deduced since for neutral particles both and are real. Realizing that

(4.82) |

it follows that

(4.83) |

so that and . Accordingly there exist two different kinds of neutral particles, namely

- neutral particles with positive charge parity, ie. ,

- neutral particles with negative charge parity, ie. ,

Neutral particles are thus eigenfunctions of the charge conjugation operator, while charged particles are not.

2004-03-18