The following notation will be handy when dealing with spin-0 fields. For scaler functions and ,

(2.25) |

The Dirac delta-function can be defined using

(2.26) |

A useful property of the Dirac delta-function is

(2.27) |

where . One particularly useful example of the above general relationship is

where is a constant.

The delta-function in three dimensions is often written as

(2.29) |

Cauchy's integral formula is

(2.30) |

where the direction of the contour of integration is clockwise. A counter-clockwise direction of integration results in an over all minus sign.

Integration by parts gives

(2.31) |

The ``surface term'' can usually be neglected.

2004-03-18