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A Green's function is the impulse response of an inhomogeneous differential equation defined on a domain, with specified initial conditions or boundary conditions, thereby restricting that equation's fundamental solution. In QFT, it is essentially the propagator.

3 votes

Conditions to determine the Green's function for scattering phenomena

"My problem here is the following: to find G we need boundary conditions of the problem. I can't understand, though, what boundary conditions we should impose here. So to solve scattering prob …
dolun's user avatar
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6 votes

How is Lippmann-Schwinger equation derived?

Most of the time, an (elastic) scattering problem can be reduced in : An incoming initial wave / quantum state $|\phi\rangle$, which most of the time is taken to be a plane wave / free state $|\text …
dolun's user avatar
  • 2,598
11 votes
Accepted

How is Green function in many-body theory introduced?

Because these are actually Fourier transform of the usual Green functions. Consider the Schrödinger equation : $$ \hat{\mathcal{H}}|\Psi(t)\rangle=\mathrm{i}\partial_t|\Psi(t)\rangle $$ The general so …
dolun's user avatar
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19 votes

What do the poles of a Green function mean, physically?

Let me expand a little more on what Craig Thone just said : Consider the energy/frequency-dependent Green function : $$ \tilde{G}(\omega)=\frac{1}{\omega-(a-\mathrm{i}b)} $$ with one single pole in $ …
dolun's user avatar
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