{wiki}

The <Feynman propagator> is a vacuum time-ordered two-point function, with the conventional overall factors stated. For a free <real scalar field>, $\langle0|T\phi(x)\phi(y)|0\rangle$ has momentum-space form $i/(p^2-m^2+i0)$ in the usual Minkowski convention.

<Time ordering> places the later field to the left, and the pole prescription selects the vacuum <boundary condition>. The <propagator> is the <Green function> used for internal lines in perturbative amplitudes; it is not a directly measured <probability> for a <particle> to follow a particular path. It can be nonzero at spacelike separation without enabling superluminal signalling. Causal response is instead organized by the <retarded Green function> and local <commutators>, so these different two-point functions must not be interchanged.


 Feynman propagator (source code)