Reading some books of quantum field theory (c.f. LH Ryder. 'Quantum Field Theory') it seems that the concept of path integrals in quantum mechanics may be extended to the field theory using the concept of propagators. Without going into details the photon propagator via path-integral method is calculated:
$$ D_F(k)_{\mu\nu}=-\frac{g_{\nu\mu}}{k^2} $$
My question is: does this propagator really 'propagates the photon'? Can I understand the propagator in QED in the sense of an initial state in a previous time going into a final state?
$$ \Psi(q,t)=\int K(qt,q't')\Psi(q',t')\,d^3q'\,. $$
if so, why does it not look like the Huygens-Fresnel principle, since Rayleigh-Sommerfeld equation shows how the electromagnetic field propagates in the free space?
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