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.
Questions tagged [greens-functions]
863 questions
7
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2 answers
spectral functions
Please, I would like to understand why you call the function $A(k,\omega)$ (here :The Spectral Function in Many-Body Physics and its Relation to Quasiparticles ) a spectral function? For me, as a mathematician, a spectral function is a function…
AJA
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3
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1 answer
Matsubara Green Function vs Real Green Function
Why is the Matsubara Green function $\mathscr{G}(i\omega_n)$ equal to the retarded Green function (also the linear response susceptibility) $\chi(\omega+i\epsilon)$ under the substitution $i\omega_n \mapsto \omega+i\epsilon$.
I understand that you…
Andrew Yuan
- 2,064
3
votes
2 answers
Help with understanding Green's Functions
I. The Green's Function Method
The Green's function is immensely useful as a tool in Solid State Physics. Using a Green's function, one can compute all relevant data from a physical system. For example, the Green's function for the time-independent…
David Roberts
- 987
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1 answer
D'Alembertian and Laplacian Green's Fucntions
There is a way to obtain the Green's Function for the Laplacian as a limit of the Green's function of the D'Alembertian?
For the Laplacian ($-\nabla^2$) we have
$$ G_1(\vec X) = \frac{1}{4\pi X}$$
And for the D'Alembertian ($\Box$) using the…
Erich
- 934
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1 answer
Search for differential equation from Green function
Let's consider the following:
We have a Green function $G$, and we want to know what linear differential equation is solved by $G$.
How to do this? The question is: If I know $G$, then is there a method that allow to solve equation $LG=\delta$…
Tomek
- 63
2
votes
2 answers
In which sense is the linear operator the inverse of a Green function?
This is really a math question in which I will expose to the world my apparent lack of expertise with Greens functions, but it has appeared in a physics context so I guess it might be useful to somebody else. I am studying the $O(N)$ non-linear…
Yossarian
- 6,017
1
vote
1 answer
How to calculate the inverse of the function?
When dealing with constraint systems, we use dirac bracket instead of poisson bracket. In that procedure, we first find constraints $\Lambda_i$ and gauge $\Omega_i$, then we calculate the matrix consisting with their commutation, and the inverse of…
1or2or3
- 75
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Fourier transforming a Dyson equation
I have a Dyson equation for a Green's function that comes in this form:
$$
G[t,x_f;0,x_i]=G_0[t,x_f;0,x_i]+i\int_\Omega\int_0^t\ dx\ d\tau\ G_0[t,x_f;\tau,x]xG[\tau, x;0, x_i]
$$
For convenience, I'd like to Fourier transform it in time. Keeping in…
Okarin
- 421
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Greens function application Abrikosov - QFT in Statistial Physics
I am looking at section 7 of the textbook mentioned in the title, and he defines the G as
$$G\equiv -i\langle T \psi_a(x)\psi_b(x')\rangle$$
Then says that we can construct j from this as
$$j=\pm\frac{1}{2m} \lim_{r\rightarrow r'}\lim_{t'\rightarrow…
yankeefan11
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Spectral function and response function
Could someone explain the concept of spectral function, spectral weight and linear response function? How are they useful in describing physical processes? Thanks!!
ZR-
- 493