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What does a completely negative Greens function in frequency mean?

What can a Greens function of frequency mean when it is always negative? The Greens function is for the photons as the following: (It's derived by Matsubara method to enter the thermal effects and the ...
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1answer
40 views

Understaning Euclidean Green's function

Consider a scalar field coupled to a source $$(\Box - m^2)\phi(x) = -J(x)\tag{1}.$$ Then, the response of the source is determined by the Green's function $G(x-y)$, which satisfies $$(\Box - ...
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39 views

Green function for single impurity

I am working on the first problem on self-consistent T-matrix approximation in Chapter 5 of Condensed Matter Field Theory by Altland and Simons. This is on page 234 of the textbook. I have some ...
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0answers
28 views

Green function for interacting system

If we can diagonalize our interacting Hamiltonian then can we write a Green's function like we do for a non-interacting system? Green's function here means Matsubara in frequency-momentum space, ...
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0answers
35 views

How can I determine the convergence of self energy in Green's function

I want to solve for the Green's function (in the context of many body theory) but I have a question. After the determination of the retarded Green's function and the lesser Green's function we ...
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1answer
53 views

1-particle non-interacting Green function

At $T=0$ in the non-interacting case the $1$-particle Green function for an electron in the excited state $\lambda$ (empty band) is of the form \begin{eqnarray} G^{(0)}(\lambda,t-t') = -i \theta(t-t') ...
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38 views

Retarded Green function and the gravitational field of a point particle

I'm trying to understand a calculation by Aichelburg and Sexl of the gravitational field of a point particle. Linearizing the Einstein field equations in the usual way (that is, supposing a metric of ...
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1answer
61 views

Why do we have different signs before the delta on the Klein-Gordon and the Dirac Green's function equation?

Let's read equation (2.56) on Peskin & Schroeder $$(\partial^2+m^2)D_R(x-y)=-i\delta^4(x-y).$$ Let's look now to equation (3.118) $$(i\gamma^{\nu}\partial_{\nu}-m)S_R(x-y)=i\delta^4(x-y).$$ ...
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26 views

intervalley optical phonon scattering

Is there any difference between intravalley and intervalley optical phonon scattering self-energies in NEGF method?(except that electron-phonon coupling constants)
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27 views

Electron transmission in Landauer formalism: why just imaginary part?

In Landauer formalism the electron transmission function is defined as $T = Tr(G_M^\dagger\Gamma_LG_M\Gamma_R)$ where $G$ are Green's function of subsystems, index $L$ and $R$ means subsystem of ...
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101 views

Green's function for a dielectric with a charge [closed]

Suppose there are two infinite planes, one in $z=a$ and the other in $z=b$, with $a<b$. Between the planes, there is a dielectric medium with constant $\epsilon_1$. The differential equation for ...
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1answer
93 views

How to choose the Correct Green's Function?

In order to solve the Green’s function of the Helmholtz operator $$(\nabla^2+k^2)G(\vec r-\vec r’)=\delta^{(3)} (\vec r-\vec r’)$$ one can obtain four different Green’s functions corresponding to four ...
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58 views

Violation of causality in classical physics possible?

In quantum field theory, the Feynman propagator $\Delta_F(x-y)$ does not vanish (though exponentially suppressed $\sim \exp{(-|\vec x-\vec y|)}$) outside the light cone. But Feynman's ...
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0answers
41 views

Physical meaning behind causal massless scalar propogator

I know that for a scalar massless field in $(3+1)$ spacetime that: $$ \langle 0 | \phi(x) \phi(y) | 0 \rangle \propto |x-y|^{-2} = (-(t_x-t_y)^2 + (\vec{x}-\vec{y})^2)^{-1}. $$ I also know that $$ ...
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1answer
117 views

Green function for simple harmonic oscillator

I'm interested in examples on how to use Green function (GF)for simple harmonic oscillator (SHO)? I am from undergrad physics, so I need a fundamental math and quantum mechanical application of GF ...
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58 views

Greens function/resolvent of hydrogen Hamiltonian

Let $H$ be the Hamiltonian for the nonrelativistic hydrogen atom, i.e. $$H=-\frac{1}{2}\Delta-\frac{1}{r}$$ I am searching for an asymptototic expansion of the Greens function or respectively the ...
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2answers
76 views

How to get the relation for dependence of anomalous dimension on regularization?

Here is the anomalous dimension: $$ \gamma_{\Gamma}(t, g) = \left[\frac{\partial }{\partial t}\ln \left(Z_{\Gamma}(t , g) \right)\right]_{t = 1}, $$ where $Z_{\Gamma}$ is renormalization factor which ...
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41 views

Benefit of using Matsubara Green function

Physicists often calculate Matsubara Green function and then perform an analytic continuation $i\omega_n \rightarrow \omega +i\eta$ to obtain the retarded Green function. Why is doing so better than ...
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0answers
77 views

Integral over a product of two Green's functions

Need some help here on a frequently encountered integral in Green's function formalism. Forgive me since I am a junior student. I have an integral/summation as a product of a retarded and advanced ...
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1answer
95 views

Are constant terms in second-quantization relevant?

I have a rather broad question and a specific problem. Let's take a orthonormal single-particle basis $\{ \vert i \rangle \}$, a simple single-particle Hamiltonian $$\tilde{H} = \sum_{i, j} h_{i j} ...
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1answer
55 views

Can someone show me how Green's function would apply for this simple case?

I'm reading up on some stuff on basic electrostatic here: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/laplace.html Can someone use Green's function to show me the form of $V$? Update: I ...
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18 views

Green's function for moving solidification front

Consider a liquid solid interface $z =\zeta(x,t)$ moving at constant speed $v$, for a two dimensional problem. Due to solidification interface is changing it position. For simplicity heat ...
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96 views

Variations of S-matrix functional and Feynman diagrams in Weinberg QFT

Weinberg on p. 287 of his QFT vol. 1 introduces the extended interaction operator: $$ \tag 1 \hat{V}(t) \to \hat{V}(t) + \sum_{a}\int d^{3}\mathbf x \hat{o}_{a}(\mathbf x ,t)\varepsilon_{a}(x). $$ ...
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38 views

simplification of Green's intergral for diffusion

\begin{eqnarray} I_1 = \int^{\infty}_{0} \frac{1}{\tau}d\tau \int^{+\infty}_{-\infty} \exp\left[-\frac{p}{2\tau}(x-x')^2 + (z-z' + \tau)^2\right]dx' \end{eqnarray} where, $p$, $x$ $z$ and $\tau$ are ...
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83 views

The n-point Green functions and Heisenberg picture

Let's have the S-matrix: $$ S_{\beta \alpha} = \langle \beta | \hat{S} | \alpha\rangle . $$ Here $|\alpha \rangle , | \beta \rangle$ are $t \to \mp \infty$ limit of the free states, $\hat {S} = ...
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0answers
75 views

How to calculate the 2-point function of gravitons?

I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. So how to calculate it? In which book can I find the ...
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52 views

Sum of Green's functions in Condensed Matter

I am working on the Ginzburg-Landau model for Charge density waves, and I am carrying out the sum of Green's functions to calculate the terms in the GL model. I have the following question: Is the ...
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49 views

Bound states and continua in the spectral function

Okay, let me try hard to pose this question as clear as I can. Let's take a quantum system where a single charge carrier interacts with a bosonic mode. Examples would be the Holstein model where a ...
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3answers
124 views

Analytical problems with Green's function

I have a question about the right definition of the Green's function in physics. Why do we introduce (or not) an infinitesimal, positive number $\eta$ to the following definition: $$\left[ ...
5
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1answer
95 views

Particle/Pole correspondence in QFT Green's functions

The standard lore in relativistic QFT is that poles appearing on the real-axis in momentum-space Green's functions correspond to particles, with the position of the pole yielding the invariant mass of ...
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1answer
88 views

Green functions in QFT

What is the sense of Green function $$ \langle | \hat {T}(u_{1}(x_{1})...u_{n}(x_{n})\hat {S})|\rangle , \quad \hat {S} = \hat{T}e^{i\int \hat {L}(x)d^{4}x} ? $$ How is it connected with scattering ...
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1answer
99 views

George Green's definition of Green's function

This is a curious question about the way George Green could have defined his Green's function. All the definitions I see have only Dirac-delta $\delta(x−x′)$ function as their source on the RHS. But ...
5
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1answer
309 views

Numerical analytic continuation for Green's function

Recently, I happened to hear about the possibility of doing analytic continuation numerically. That sounds attractive for the ubiquitous $\mathrm{i}\omega_n\rightarrow\omega+\mathrm{i}0^+$ procedure, ...
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193 views

Green's function for the inhomogenous Klein-Gordon equation

I'm trying to solve the massive Klein-Gordon equation in good old Minkowski space-time: $$(\square + m^2) \phi = \rho(t,\mathbf{x})$$ where $\square = \partial_{\mu} \partial^{\mu} = \partial_{t}^2 - ...
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82 views

Langreth rules and Keldysh formalism

I am trying to confirm the proof of Langreth's theorem / rules as seen in http://www.iue.tuwien.ac.at/phd/pourfath/node52.html . My problem is equation 3.55. I would do it like this: $\int_{C_{1}} ...
2
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1answer
104 views

What is the generating functional for a scalar theory with two different (interacting and real) fields?

My question is specifically about how to use sources? For an interacting theory with one field, one puts a $J(x)\phi(x)$ term in the exponential in the path integral for $W[J]$. I now have two ...
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1answer
147 views

Simple question regarding the Green's function for the diffusion equation

The differential operator for diffusion in three dimensions is given by $\partial_t - k \nabla^2$ where $k$ is a constant. The Green's function is (according to Wikipedia) $$\theta(t)\left( ...
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1answer
119 views

Closed expression for the Green's function for 2D Helmholtz equation over rectangular domain

I have to use the Green's function for the 2D Helmholz equation $$(-\nabla^2 - E) \psi(x, y) = 0$$ on the rectangular domain $[0, L_x] \times [0, L_y]$ with Dirichlet boundary conditions: $$\psi(0, y) ...
3
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1answer
144 views

Physical interpretation of Green's theorem with Dirichlet boundary condition

The potential is given by $$\Phi(\mathbf{x})=\int_V d^3x' G_D(\mathbf{x},\mathbf{x'})\rho(\mathbf{x'})-\frac{1}{4\pi}\oint_S d^2x'\frac{\partial G_D(\mathbf{x},\mathbf{x'})}{\partial ...
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0answers
28 views

Order of Monte Carlo integration and frequency summation

I am currently trying to calculate an integration formula of a linear response function by Monte Carlo method. It is a multiple integration over three 3D vectors, i.e., nine dimensions in all. And ...
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1answer
114 views

Green function two solutions questions

I am having some trouble with Green functions in electrostatics What is the meaning of this trick: Given $$\vec{\nabla}^2 V(\vec{r}) = \frac{-1}{\varepsilon_0}\rho(\vec{r}) = ...
2
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2answers
157 views

Lippmann-Schwinger Equation with Outgoing Solutions

I'm reading about Green's functions and how the Lippmann-Schwinger equation eventually leads to the textbook expression for the form of wavefunctions in the far radiation zone after scattering by a ...
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0answers
63 views

Derivation of the Landauer formula for phonons using Nonequilibrium Green's functions

I am currently trying to understand this paper: http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.255503 I really like their derivation of the Landauer formula for phonons using ...
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1answer
133 views

Feynman Green Function in D=2 for D'Alembertian

I'm trying to obtain the Feynman Green Function (i.e. I'm using the Feynman Causal prescription to compute the green function) for the D'Alembertian in D=2, I'm finding $$G^{(2)}_F (t; \vec x) = ...
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1answer
54 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
139 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
63 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 ...
2
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1answer
187 views

An Electric Potential Glued to a Cube-Shaped 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-shaped insulator so that outside of the insulator the field is the same as a point ...
3
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1answer
71 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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75 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 ...