Editing Propagator (section)

====Explanation using limits====
This can be made clearer by writing the propagator in the following form for a massless particle:
<math display="block">G^\varepsilon_F(x, y) = \frac{\varepsilon}{(x - y)^2 + i \varepsilon^2}.</math>

This is the usual definition but normalised by a factor of <math>\varepsilon</math>. Then the rule is that one only takes the limit <math>\varepsilon \to 0</math> at the end of a calculation.

One sees that 
<math display="block">G^\varepsilon_F(x, y) = \frac{1}{\varepsilon} \quad\text{if}~~~ (x - y)^2 = 0,</math>
and
<math display="block">\lim_{\varepsilon \to 0} G^\varepsilon_F(x, y) = 0 \quad\text{if}~~~ (x - y)^2 \neq 0.</math>
Hence this means that a single massless particle will always stay on the light cone. It is also shown that the total probability for a photon at any time must be normalised by the reciprocal of the following factor:
<math display="block">
\lim_{\varepsilon \to 0} \int |G^\varepsilon_F(0, x)|^2 \, dx^3 
 = \lim_{\varepsilon \to 0} \int \frac{\varepsilon^2}{(\mathbf{x}^2 - t^2)^2 + \varepsilon^4} \, dx^3
 = 2 \pi^2 |t|.
</math>
We see that the parts outside the light cone usually are zero in the limit and only are important in Feynman diagrams.