How does the photon propagator in Feynman diagrams relate to massless particles?

[Silviu]

Hello! I have a question about the photon propagator in Feynman diagrams. I am looking over a brief derivation (probably there are some details missing), so basically it starts from Proca equation for a mass 0 particle, then it assumes Lorentz condition and in the end it obtains: $(-p^2g_{\mu\nu})A^\nu=0$, from which the propagator is $-i\frac{g_{\mu\nu}}{p^2}$. I understand the math, but I am a bit confused about the physics. So it starts with the Proca equation for a mass 0 particle, but the photon that is the propagator is off-shell (hence why p is different from 0) so it has mass. So how can you start from an equation for a massless particle and obtain a particle with mass?
Thank you!

 

[nrqed]

Hello! I have a question about the photon propagator in Feynman diagrams. I am looking over a brief derivation (probably there are some details missing), so basically it starts from Proca equation for a mass 0 particle, then it assumes Lorentz condition and in the end it obtains: $(-p^2g_{\mu\nu})A^\nu=0$, from which the propagator is $-i\frac{g_{\mu\nu}}{p^2}$. I understand the math, but I am a bit confused about the physics. So it starts with the Proca equation for a mass 0 particle, but the photon that is the propagator is off-shell (hence why p is different from 0) so it has mass. So how can you start from an equation for a massless particle and obtain a particle with mass?
Thank you!

Off-shell means that the four momentum does *not* obey $P^2 =m^2$ so the fact that $P^2 \neq 0$ does not mean that it is massive, it is still massless.