For an arbitrary direction of , we may write in terms of the direction cosines:

(5.144) |

Raising the index makes anti-symmetric. Also is anti-symmetric. Therefore

(5.145) |

From the properties of the matrices, we have

(5.146) |

The finite spinor transformation for a general Lorentz boost becomes

For a Lorentz boost . However, by expanding in a power series, it has the property

(5.148) |

This can also be generalized to include rotations.

2004-03-18