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1answer
27 views

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 $$ G_1(\vec X) = \frac{1}{4\pi X}$$ ...
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0answers
67 views

Green Function for Proca Equation

I have tried to find a retarded and advanced Green function for Proca field equation. $(\Box - \mu^2)A^{\mu}=J^{\mu}$ where $\mu$ is the mass term. How I did it: first: I made Fourier ...
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0answers
53 views

Why Green's function will diverge at the same spacetime point?

In $d+1$ dimensional quantum field theory, the 2-point Green's function will diverge at the same spacetime point when $d\geq1$. When $d=0$, $\phi(t)=q(t)$, that is the case of QM, and 2-point Green's ...
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1answer
91 views

An Electric Potential Glued to a Cubic Insulator to Replicate a Point Charge: Charge Distribution

I have been going back over this problem with a friend for the better part of a day: A potential is glued to a cube insulator so that outside of the insulator the field is the same as a point ...
3
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1answer
60 views

Correct formula to express the potential generated by a single layer charge distribution

Assume that the closed surface $S$ encircles a volume $V$, and that a surface charge with density $\sigma$ ("single layer") is distributed over $S$. My question regards the electrostatic potential ...
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0answers
42 views

Wave equation for de Sitter invariant Green's functions

In several papers on QFT in de Sitter space (curvature set to $1$) it is asserted that the Klein-Gordon equation obeyed by the two point function of the free fields: $$(\square-m^2)G(x_1,x_2)=0 $$ can ...
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0answers
29 views

How to deal with $\vec{j}\cdot\vec{A}$ or $\rho A^2$ interaction when utilizing Kubo formula? Gauge invariance?

If there exist electromagnetic fields in solids, electrons can feel interactions like $\vec{j} \cdot \vec{A}$ or $\rho A^2$ (these are not regarded as perturbations). But these are not gauge ...
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1answer
85 views

How do you solve Laplace's equation for a parallel plate capacitor?

I would like to find the analytic solution to the problem of two plates of opposite electric potential. I have already solved this numerically as shown in the picture below. I'm also wondering what ...
2
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1answer
83 views

Derivation of Green's Function for Wave Equation

In the textbook Modern Methods in Analytical Acoustics (Crighton-1992) the following relates the 3D Green's function in the time-domain to the frequency domain g(x-y): I cannot see how the ...
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2answers
114 views

Field Strength Renorm in Peskin&Schroeder

On page 237 in PS we have (the unnumbered equation after eq. 7.58) $$\mathcal{P} \sim \frac{iZ}{p^2-m^2-iZ\,\mathrm{Im}M^2(p^2)}$$ but after deriving it myself I obtained $$\mathcal{P} \sim ...
0
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1answer
63 views

How to get conductivity from Green function $\mathcal{G}(x_1,x_2,\tau)$ of inhomogeneous system?

I'd like to study an inhomogeneous system, i.e., momentum is not a good quantum number therein. Therefore, I tried to calculate temperature Green functions like $\mathcal{G}(x_1,x_2;\tau)$, or its ...
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2answers
131 views

A conceptual question about Green's function's treatment of interaction

Here we have electron gas and some other stuff. We expand the Hamiltonian to the 1st order of one single harmonic oscillator's displacement $\vec{u}$. Its equilibrium position is at the origin. Then ...
5
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1answer
225 views

Green's function in path integral approach (QFT)

After having studied canonical quantization and feeling (relatively) comfortable with it, I have now been studying the path integral approach. But I don't feel entirely comfortable with. I have the ...
1
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1answer
101 views

Finding Green function using eigenfunction expansion method

Given the Dirichlet boundary condition, I am to show that the functions that satisfy $(\nabla ^2 + k_{lmn}^2) \psi_{lmn} (x,y,z) = 0$ are given by $\psi_{lmn} = (\frac{\pi}{2x})^{1/2} J_{l+1/2}(x) ...
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0answers
89 views

Confusion regarding field operators

Second quantisation of the scalar field leads to an algebra of quantum field operators $$ [\phi(x),\phi(y)] = 0, \ \ [\pi(x), \pi(y)] = 0, \ \ [\phi(x),\pi(y)] = i\hbar \delta(x-y). $$ Where the field ...
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0answers
57 views

Interpretation in Fourier-Laplace domain

The Green's function describing the distribution of particles sent from $\def\v#1{\boldsymbol{#1}}\def\u#1{\hat{\v#1}}\v r=0$ at $t=0$ uniformly in every directions is, in two dimensions $$ ...
4
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2answers
115 views

In Jackson's expression for the electrostatic Green function, why is the Laplacian taken with respect to the primed coordinates?

Jackson writes, The function $1/|\mathbf{x} - \mathbf{x}'|$ is only one of a class of functions depending on the variables $\mathbf{x}$ and $\mathbf{x}'$, and called Green functions, which satisfy ...
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3answers
72 views

Proof for a time-ordering equation in Negele & Orland (1998)

Let $T$ be the time-ordering operator which orders operators $A_1(t_1), A_2(t_2), \ldots$ such that the time parameter decreases from left to right: $T[A_1(t_1) A_2(t_2)] = A_2(t_2) A_1(t_1)$ if $t_2 ...
3
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1answer
95 views

Retarded (Advanced) GreenFunction [closed]

I need to show that Green Function: $\displaystyle G(\vec{r},t;\vec{r}^{\prime},t^{\prime}) = \frac{\delta(t-t^{\prime}\pm |\vec{r}-\vec{r}^{\prime}|\,/c)}{|\vec{r}-\vec{r}^{\prime}|}$ Obeys ...
3
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2answers
130 views

One-point Green's function

Why is one-point Green's function for scalar field equal to zero? Can one prove it using path integral formalism?
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2answers
422 views

Propagator for Dirac equation in real space

I'm interested in the retarded propagator for a free massless Dirac fermion, i.e. solutions $ψ$ to the inhomogeneous PDE $$ (∂_t- \nabla·\vec σ) ψ(x,t) = f(x,t) $$ with boundary conditions $$\quad ...
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0answers
67 views

A question about inverse Green's function

(The background is in a book, An introduction to String Theory and D-brane Dynamics 2nd, by Richard J Szabo p87, Eq. (6.31)) Given $$N(\theta,\theta')= - \frac{1}{\pi} \sum_{n=1}^{\infty} \frac{ ...
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1answer
102 views

Two point function for massless boson in 2 dimension

Is it true that two point function for massless boson theory in 2 dimension is a constant? That is to say it is independent of the distance between the two points?
5
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1answer
386 views

A curious issue about Dyson-Schwinger equation(DSE): why does it work so well?

This question comes out of my other question "Time ordering and time derivative in path integral formalism and operator formalism", especally from the discussion with drake. The original post is ...
1
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1answer
246 views

Symmetry factor of a second order four point function term of the $\phi^4$ theory

I am reading Cheng and Li. On page 9, it is written that the coefficient $\frac{1}{2 \cdot (4!)^2}$ for the second order term of the four point function becomes just $\frac{1}{2}$ for the following ...
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2answers
880 views

Time ordering and time derivative in path integral formalism and operator formalism

In operator formalism, for example a 2-point time-ordered Green's function is defined as ...
3
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1answer
63 views

Forward-scattering for a single impurity in an infinite system

I'm slightly confused with the following situation: Suppose you have an electron in a tight-binding model, and let's say we are in one dimension with $N$ lattice sites. Add to this a single ...
6
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2answers
227 views

Is the Green function a prescription for a connection?

I'm trying to learn connection on principal fibre bundle. As far as I can see, the connection is just a given prescription for the displaced field/function on the base space to remains on the ...
4
votes
1answer
211 views

Solving the differential equation of a beam under moving load using green functions

i started working on this paper and i didnt understand one part of it , the problem is : Solve this equation using green functions : $$ EI {\partial^4 y(x,t)\over\partial x^4}+\mu ...
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0answers
132 views

Problems related to Green's function? [closed]

My teacher told me to do a research studying some physics problems that has connection with Green's function on solving differential equations (with programmed numerical solutions) in my final year ...
6
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1answer
231 views

Differential equation (Greens function) satisfied by the kernel using path integrals

I'm reading Feynman and Hibbs, Quantum Mechanics and Path Integrals. How do I show that the kernel $$\tag{2-25} K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$$ satisfies the ...
7
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1answer
225 views

Correlated three-particle Green Function

I know the relationship between normal and correlated two-particle Green Functions for fermions: $$G_c(1,2,3,4)=\Gamma(1,2,3,4)=G(1,2,3,4)+G(1,3)G(2,4)-G(1,4)G(2,3)$$ Also known as irreducible ...
3
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0answers
134 views

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 ...
2
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2answers
900 views

Greens function in EM with boundary conditions confusion

So I thought I was understanding Green's functions, but now I am unsure. I'll start by explaining (briefly) what I think I know then ask the question. Background Greens are a way of solving ...
3
votes
1answer
268 views

Deriving the reduced Green's functions in Polchinski's volume 1

In equation 6.2.7, Polchinski defines his reduced Green's functions $G'$ on the 2-manifold to satisfy the equation, $$ \frac{-1}{2\pi \alpha '}\nabla ^2 G'(\sigma_1, \sigma_2) = ...
4
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1answer
224 views

Boundary conditions of relativistic wave solutions?

If you take Einstein's field equations, \begin{equation} R_{\mu\nu}-\tfrac{1}{2}g_{\mu\nu}R = -\kappa T_{\mu\nu}, \end{equation} and you insert the metric \begin{equation} g_{\mu\nu} = \eta_{\mu\nu} ...
1
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1answer
72 views

Trouble following the Saclay method (spectral representation of thermal Green functions)

Note: I just answered my own mathematical question by writing it up, but I thought I'd share it anyway in case someone else has a similar difficulty. :) I'm still left with my real physical question: ...
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2answers
290 views

Help with Greens function/Fourier transformation to solve screened Poisson equation

I am having trouble getting from one line to the next from this wiki page. I am referring to the text line Green's function in $r$ is therefore given by the inverse Fourier transform, where ...
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0answers
287 views

How to find the Green's Functions for time-dependent inhomogeneous Klein-Gordon equation?

I'm trying to find the Green's functions for time-dependent inhomogeneous Klein-Gordon equation which is : \begin{align*}‎‎ \left[ -‎ ‎\nabla ‎^2 + ‎‎‎‎\frac{1}{c^2} ‎‎\dfrac{\partial ^2}{\partial ...
5
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1answer
497 views

Analytic continuation of imaginary time Greens function in the time domain

Consider the imaginary time Greens function of a fermion field $\Psi(x,τ)$ at zero temperature $$ G^τ = -\langle \theta(τ)\Psi(x,τ)\Psi^\dagger(0,0) - \theta(-τ)\Psi^\dagger(0,0)\Psi(x,τ) \rangle $$ ...
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2answers
851 views

Sources to learn about Greens functions

For a physics major, what are the best books/references on Greens functions for self-studying? My mathematical background is on the level of Mathematical Methods in the physical sciences by Mary ...
11
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1answer
454 views

Boundary conditions / uniqueness of the propagators / Green's functions

My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields. It is well known that the Green's function for the Laplace ...
2
votes
2answers
361 views

Correlation functions in thermal field theory etc

Suppose I am studying a field theory at finite temperature or some black hole formation scenario from boundary theory perspective in the sense of AdS/CFT. How is it possible to gain information about ...