The following notation will be handy when dealing with spin-0 fields. For scaler functions and ,
The Dirac delta-function can be defined using
A useful property of the Dirac delta-function is
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
Cauchy's integral formula is
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
The ``surface term'' can usually be neglected.