Propagators

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Propagators

With each internal line connecting two vertices one has to be assoicated with a propagator:

$\begin{picture}(240,5) \Text(0,0)[l]{\bf Spin-0} \put( 60,0){\line(1,0){20}} \p... ...1,0){8}} \put(180,0){\line(1,0){20}} \put(220,0){\line(1,0){20}} \end{picture}$

$\begin{displaymath} \frac{i}{p^2-m^2} \end{displaymath}$

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$\begin{picture}(240,5) \Text(0,0)[l]{\bf Spin-1/2} \put( 60,0){\vector(1,0){92}} \put(152,0){\line(1,0){88}} \end{picture}$

$\begin{displaymath} \frac{i}{\not{\;\!\!\!p}-m} = i\frac{\not{\;\!\!\!p}+m}{p^2-m^2} \end{displaymath}$

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$\begin{picture}(240,40)(0,-20) \Text(0,0)[l]{\bf Photon} \put( 60,0){\line(0,1){... ....1}} \put(82.5,-20){\line(1,0){0.1}} \Photon(60,0)(240,0){20}{6} \end{picture}$

$\begin{displaymath} \frac{i}{k^2}\left( -g^{\mu\nu} + (1-\zeta) \frac{k^\mu k^\nu}{k^2} \right) \end{displaymath}$

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for a general $\zeta$ gauge. Calculations are usually performed in Lorentz or Feynman gauge with $\zeta=1$ and photon propagator

$\begin{displaymath} \frac{-ig^{\mu\nu}}{k^2} . \end{displaymath}$

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Douglas M. Gingrich (gingrich@ ualberta.ca)
2004-03-18