Thread: Very simple QFT questions View Single Post
P: 1,135
 Quote by meopemuk It seems to be well-established that a wave function of a localized particle spreads out faster than the speed of light.
No such superluminal propagation of the wave function shows up neither
with a concise analytical treatment giving exact solutions in configuration
space, nor with extensive numerical simulations. See my old post above.

The simplest way to convince oneself may be this series development
of the Klein Gordon propagator:

$$\frac{1}{p^2-m^2}\ =\ \frac{1}{p^2}+\frac{m^2}{p^4}+\frac{m^4}{p^6}+\frac{m^6}{p^8}+.....$$

Which becomes the following operator in configuration space:

$$\Box^{-1}\ \ -\ \ m^2\Box^{-2}\ \ +\ \ m^4\Box^{-3}\ \ -\ \ m^6\Box^{-4}\ \ +\ \ ....$$

Where $$\Box^{-1}$$ is the inverse d'Alembertian, which spreads the wave function
out on the lightcone as if it was a massless field. The second term then
retransmits it, opposing the original effect, again purely on the light cone.
The third term is the second retransmission, et-cetera, ad-infinitum.

All propagators in this series are on the lightcone. The wave function does
spread within the light cone because of the retransmission, but it does
never spread outside the light cone, with superluminal speed.

Regards, Hans.