# Questions tagged [greens-functions]

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.

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### Born approximation for 1D scattering using Green's function

For $1D$ scattering, we can write a recursive equation for the wave function: $$\psi(x) = Ae^{ikx} + \int dx'\frac{e^{ik|(x-x')|}}{2ik}\frac{2m}{\hbar^2}V(x')\psi(x')$$ I am trying to show that ...
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### Explicit Form of Feynman Propagator for a Scalar Field in Position-space: Derivation Details

This is Problem (6.1) from Schwartz's QFT and the Standard Model. I am trying to directly calculate, by performing the integral over momenta, the explicit position-space expression of the Feynman ...
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### Computing inverse kinetic operator for in-in formalism

Consider the kinetic operator in in-in formalism. \begin{align} -\frac{1}{2} \int_{x, y} \phi^{A}_{x} K^{AB}_{x, y} \phi^{B}_{y} \end{align} where $K^{AB}$ is the kinetic operator with the form \begin{...
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### Calculation of $\gamma(\lambda)$ in massless renormalizable scalar field theory

In Peskin & Schroeder p.413 and 414, the Callan-Symanzik equation for a 2-point Green's function is used to calculate $\gamma(\lambda)$ for a massless renormalizable scalar field theory. The two-...
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### Some calculation in Mahan book, p73 [closed]

On page 73 of Mahan, Many-particle physics, 3rd edition, one finds $$_0\langle|S(-\infty,0) = e^{-iL}_0\langle|S(\infty,-\infty)S(-\infty,0).$$ I'm wondering why this is true, as in the previous ...
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