We introduce the coupling to an electromagnetic field to obtain an interpretation of the internal structure of Dirac particles. Consider the interaction of a point charge with an external electromagnetic field. The 4-potential is , where is a function of only. We make the usual gauge invariant minimal substitution

(5.20) |

where is the magnitude of the charge of an electron. The Dirac equation becomes

(5.21) |

or

(5.22) |

This equation contains the interaction with the electromagnetic field:

(5.23) |

where

(5.24) |

and

(5.25) |

is the classical correspondence of the relativistic velocity operator. We can see this by looking at the relativistic extension of the Ehrenfest relation:

(5.26) |

2004-03-18