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Results tagged with greens-functions
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user 65510
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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Delta function in Green's function
I am working through Altland Simons 2nd edition. On page 225 we find:
$$G_p = [1 - G_{0, p} \; \Sigma_p]^{\, -1} \, G_{0, p} = [G_{0, p}^{\, -1} - \Sigma_{p}]^{-1}$$
Finally, using the fact that $[G …
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Understanding two algebra steps in Altland & Simons
I would like to understand two summations on page 184-185, where we are told that assuming $x > 0$:
$$ G_{\pm} (x, \tau) = - \frac{T}{L} \sum_{p, \omega_{\, n}} \frac{1}{- i \omega_n \mp p} e^{- i p x …
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A simple derivative
I'm working through a simple derivative in the second edition of Altland and Simons, and I keep getting the wrong answer when I take a derivative.
Given equation 5.22:
$$G_p \equiv \frac{1}{- i \omega …
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Hartree type diagrams in Altland Simons
We are told in equation 5.25:
$$F^{(2), 1} = - \frac{T^3}{L^6} \sum_{p_1, \, p_2, \, q} \; G_{p_1} \; G_{p_1 + q} \; G_{p_2} \; G_{p_2 + q} \; V(q)^2$$
$$F^{(2), 2} = \frac{1}{2} \frac{T^3}{L^6} \su …
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Prefactors for Fourier Transforms in Altland Simons
I am trying to understand how to do the Fourier Transform on pages 184 - 185 in Altland Simons(2nd ed). In particular, we are told in the problem statement part b:
$$ S[\theta] = \frac{1}{2 c} \int dx …
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Representing Green function as a coherent state path integral
I am working through the problem "self-consistent T-matrix approximation" in Altland and Simons (second edition) pg 234. One of the steps involves representing the Green function as a coherent state p …