Can I use Fourier transform of Matsubara Green's functions for imaginary...
I am learning Matsubara Green's functions using Henrik Bruus, Karsten Flensberg, Many-Body Quantum Theory in Condensed Matter Physics, An Introduction (2016). There, the authors calculated the...
View ArticleA tricky derivation accompanied by delta function
I have been reading a book on Thermal Field theory by Michel Le Bellac During the reading I have come into a seemingly trivial but indeed tricky derivation. On page 26(2.47), we are supposed too...
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The Ward-Takahashi identity in Peskin and Schroeder (page 311)
I'm working on the Ward-Takahashi identity in Peskin (page 311), but I canʻt obtain Eq.(9.105) from Eq.(9.103)According to Eq.(9.103)\begin{align}&i \partial_{\mu}\left\langle 0\left|T j^{\mu}(x)...
View ArticleSolving for gluon propagator in axial gauge
I know the two-point function is given by:$$\Gamma^{A_\mu^a A_\nu^b}(p) = -i \delta^{ab} (g_{\mu \nu} p^2 - p_\mu p_\nu + \frac{1}{\zeta}n^\mu n^\nu)$$and I am looking to solve for the inverse of this...
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Solving Wave Equation in 1+1D via Fourier Transforms with Dirac Delta...
I'm trying to use the Fourier transform method to solve the following PDE:This is a an infinite string with a pulse for it's initial condition. (At $t=0$, the string is stricken sharply so that the...
View ArticleIntuition behind retarded/causal Green's function for the 1+1D wave equation
I see that the retarded/causal Green's function for the 1+1D wave equation is$$ G(x, t \,|\, x_{0}=0, t_{0}=0) = \frac{1}{2c} H(t - |x/c|), $$(where $H$ is the Heaviside step function) which...
View ArticleGreen Function for Poisson Equation Derivation
I've read the Green function derivation for Poisson Equation (electrostatics) in this document. There are some points which are not clear for me.On page 10, the document starts with the Poisson...
View ArticleMany-body Green Functions equation
In many-body physics the concept of Green Functions is essential especially when you deal with things like superconductivity that are strictly linked to the presence of off-diagonal long-range order in...
View ArticleCombinatorics geometric series for connected two-point function
In this answer Proof of geometric series two-point function it is said: Now what about the coefficients in front of each Feynman diagram? Due to the combinatorics/factorization involved it becomes a...
View ArticleCausality and processes in QFT
We have virtual particles in quantum field theory (QFT). In general, they don't have the need to obey causality.My question is:Do the processes in QFT (electron self-energy, photon self-energy,...
View ArticleHow is Lippmann-Schwinger equation derived?
I'd like to know the derivation of Lippmann-Schwinger equation (LSE) in operator formalism and on what assumptions it is based. I consulted the Ballentine book as advised in this Phys.SE post, but I...
View ArticleSecond harmonic of Josephoson current
The expression of Josephson current including the second harmonic between two s-wave superconductors is$$ I_{J}=I_{1}sin(\phi)+I_{2}sin(2\phi) $$I try to calculate $I_{2}$ by following derivation in...
View ArticleHow to obtain Green function for the Helmholtz equation?
all.I am following Jackson's Classical Electrodynamics.At Chapter 6.4, the book introduces how to obtain Green functions for the wave equation and the Helmholtz equation. I have a problem in fully...
View ArticleZero temperature Green function as limit of finite temperature Green function
Consider a system of $N$ fermions in a periodic box $\Lambda \subset \mathbb{R}^{d}$. The Hamiltonian of the system is:$$H_{N} = \sum_{k=1}^{N}(-\Delta_{x_{k}}-\mu) + \lambda \sum_{i<...
View ArticleDifference of the Transmission Coefficient between Thermal and Charge...
The equation 57 in the reference [Jian-Sheng Wang, Jian Wang and J. T. Lu, Quantum thermal transport in nanostructures, Eur. Phys. J. B 62, 381 (2008)] explains the the transmission coefficient for the...
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Why are time-ordered Greens functions equal to retarded Greens functions at...
When I calculate a photon polarization diagram:I get the same answer:If I calculate it in equilibrium (retarded Greens functions) with finite chemical potential, in the limit of zero temperature, orIf...
View ArticleHow small is $\eta$ when we say $\eta\to 0^+$ in Green's functions
When we convert Matsubara's imaginary time Green's function to the retarded Green's function, we perform an analytical continuation by substituting $i\omega_n$ with $\omega + i\eta$, with $\eta\to0^+$....
View ArticleTime ordering and time derivative in path integral formalism and operator...
In operator formalism, for example a 2-point time-ordered Green's function is defined...
View ArticleWhy do different contours give different answers in the limit $\epsilon...
Let $\phi$ denote the Klein-Gordon field. Then its propagator $\langle 0 \mid [\phi(x), \phi(y)] \mid 0 \rangle$ can be calculated as$$\int \frac{d^4}{(2\pi)^3} \frac{-e^{-ip(x-y)}}{p^2 -m ^2}....
View ArticleGetting Feynman propagator using path integral
In QM using Feynman path integral(FPI) we derive the propagator of free particle which comes out to $$(f(t))e^{iS_{cl}/\hbar}.$$But in QFT the Feynman propagator is derived using the differential...
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