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propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum.
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Geometric series for two-point function
In deriving the expression for the exact propagator
$$G_c^{(2)}(x_1,x_2)=[p^2-m^2+\Pi(p)]^{-1}$$
for $\phi^4$ theory all books that i know use the following argument:
$$G_c^{(2)}(x_1,x_2)=G_0^{(2)} … +G_0^{(2)}\Pi G_0^{(2)}+G_0^{(2)}\Pi G_0^{(2)}\Pi G_0^{(2)}+...$$
wich is a geometric series so the formula for the exact propagator.Here
$$G_0^{(2)}$$
is the free propagator and
$$\Pi=X+Y+Z+... …
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Reducible diagrams exapansion [duplicate]
I will refomulate my question(Geometric series for two-point function) because it seems that i did not make it clear.
In order to have
$G_c^{(2)}(x_1,x_2)=G_0^{(2)}+G_0^{(2)}\Pi G_0^{(2)}+G_0^{(2)}\ …