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Tagged with correlation-functionsgreens-functions
149 questions
1vote
0answers
37views
Relativistic Propagator for multi-particle states
In non-relativistic quantum mechanics, the transition amplitude for a system of $N$ particles is given by: \begin{equation} A = \langle\vec{q}_{1}|e^{-\frac{i}{\hbar}\hat{H}t}|\vec{q}_{2}\rangle \end{...
5votes
1answer
245views
How to understand basics of propagators and Wightman function?
Professor David Tong, in QFT notes 2 at section 2.7 above eq. (2.90) writes: "Prepare a particle at spacetime point $y$. What is the amplitude to find it at point $x$? We can calculate this: $ \...
6votes
1answer
116views
Expansion of $(S_{I}[\bar{\alpha},\alpha])^n$ in the proof of the linked-cluster theorem
On P.192 of Piers Coleman's "Introduction to many body physics", he uses Sam Edwards' replica trick to show that Green's function $$G(1-2)=\sum{\text{two-leg linked-cluster diagram}}\tag{7....
2votes
2answers
166views
Charge renormalization and wavefunction renormalization in QED
In QED, we usually say that charge renormalization is a consequence of vacuum polarization, because of the virtual electron-position pairs, the bare charge is shielded. It is intuitively ...
- 453
0votes
1answer
78views
How are path integral functional derivatives taken when a single field couples to two independent sources?
I was reading a paper https://arxiv.org/abs/2005.01515 equation (1.6) about dark photon mixing and came across the lagrangian \begin{equation} \mathcal{L}_{0}=gJ_{\mu}A^{\mu}+g'J'_{\mu}A^{\mu} \end{...
2votes
0answers
33views
References on thermal QED
Can someone provide references (books, articles, etc.) where I can find discussions and the necessary expressions for the Wightman $2$-point function in thermal Quantum Electrodynamics (QED), both for ...
1vote
0answers
39views
Density-density correlator at quasi-classical approach
Consider quasiclassical 1D motion in some potential $U$. Interresting property is following correlator: \begin{equation} K_E(\Delta t,x'|x) = \int \frac{d \omega}{2\pi} G^R_{E+\omega/2}(x'|x) G^A_{E-\...
- 103
0votes
0answers
70views
Determine 3-point function by conformal symmetry
I already posted question to math stack but I haven't yet gotten answer. So, I ask here. I'd like to know a form of functions (called 3-point function) that have symmetry under some transformation. ...
2votes
0answers
60views
From real variables function to complex variables function?
I'm confused with notations physicists using. They change real variables $$(x_1,x_2,...,x_n)\in (\mathbb{R^2})^n$$ of a function to complex variables $$(z_1,z_1^*,z_2,z_2^*,...,z_n,z_n^*)\in(\mathbb{C^...
1vote
1answer
91views
Greens Function formalism for the independent boson model
This may be a very specific question, but since almost everyone seems to be quoting this book, I want to understand the derivation(s) of the solution for the independent boson model (IBM) from Mahan's ...
- 163
1vote
0answers
81views
Propagators in the Klein-Gordon theory
I am currently doing QFT to be more precise the theory of the Klein-Gordon field and I'm a bit confused about the propagators. That's how I understood it: In non relativistic quantum mechanics the ...
0votes
0answers
34views
Are Greens function infrared finite in QED?
Scattering amplitudes are infrared divergent in QED, but are Greens functions infrared finite or infrared divergent. e.g. Is the four-point function $G(x_1,x_2,x_3,x_4)=\langle\Omega|T \Big(\bar{\psi}(...
- 2,360
1vote
1answer
103views
Doubts regarding Prahar's comments on two-point correlator of free boson in 1+1D
In this answer @Prahar says that for a conformally invariant scalar field in $(1+1)$ dimensions, corresponding to a free boson, $$\log|x-y|$$ is the only dimensionally consistent equation for the two-...
- 336
8votes
1answer
1kviews
Photon propagator in path integral vs. operator formalism
I am self-studying the book "Quantum field theory and the standard model" by Schwartz, and I am really confused about the derivation of the Photon propagator on page 128-129. He starts ...
- 776
3votes
1answer
161views
Keldysh rotation and Langreth theorem
Given a (Green) function of two arguments on the Keldysh contour $g(\tau_1, \tau_2)$, we can distinguish between four cases, depending on whether each contour time lies on the forward or reverse ...
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