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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+... …
Paul Dirac's user avatar
1 vote
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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)}\ …
Paul Dirac's user avatar