Recall the parity transformation ,

(5.262) |

The parity transformation leaves the Dirac equation and all physical observables unchanged.

We now combine all three symmetries, , and

(5.263) |

to obtain

(5.264) |

with .

Since can represent a positron, we see that it is an electron moving backward in space-time and multiplied by . Thus positrons are negative-energy electrons running backward in space-time. This is the basis of the Stückelberg-Feynman form of positron theory.

For a free-particle spin-momentum eigenstate and negative energy, we see

(5.265) |

Therefore a positron wave function is a negative-energy electron moving backward in time, multiplied by .

For an arbitrary solution in the presence of electromagnetic forces, the negative energy eigenvalue equation is

(5.266) |

Carrying out the transformation gives

(5.267) |

Notice that since

(5.268) |

Therefore .

2004-03-18