Definition of the dressed propagator

[hellfire]

In section 7.3 of Ryder's "Quantum Field Theory", the "complete" or "dressed" propagator is defined to be the two-point function to all orders of the perturbation expansion. It is denoted in (7.71) as G_c^{(2)}(x, y). It changes the bare mass to the physical mass. My question is, why aren't contributions from other n-point functions considered for this definition? For example, the 4-point function contains also disconnected graphs that modify the propagator.

 

[dextercioby]

Why should they be? Both for a free and an interacting theory the propagator is the 2 point function by definition (connected or disconnected it doesn't matter, since there are only 2 spacetime points).

Daniel.

 

[hellfire]

connected or disconnected it doesn't matter, since there are only 2 spacetime points.

Thanks, this makes sense. I was somehow confused, but your comment answers exactly my question.