# Tagged Questions

A correlation function is a statistical correlation between random variables at two different points in space, time, or other parameter space, usually as a function of the variable distance between these points. In QFT, field autocorrelation functions are propagators, so use the "propagator" tag, ...

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### Three-body correlation function in kinetic theory

In Kinetic Theory, one studies the evolution of a system of $N$ particles interacting with each other. We use the notation $\boldsymbol{w}_{i}$ to describe the coordinates in phase-space of each ...
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### Autocorrelation of noise - negative correlation

I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an ...
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### Coulomb potential

It is known that the Coulomb potential can be obtained by Fourier transform of the propagator from E&M. Is this because one of Maxwell's equations have the form $\nabla \cdot \mathbf{E}=\rho$?
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### Can one compute the vibrational spectrum of a bond by the Fourier transform of the dipole moment vector autocorrelation function $C_{\mu\mu}(t)$?

Is it true that one can calculate the vibrational spectrum of a bond by the Fourier transform of the dipole moment vector autocorrelation function $C_{\mu \mu}(t)$? For example, suppose that I have ...
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### Physics of detection of coherent light in an incoherent background using the more compact Fabry Perot interfeometer?

I read University Of California Berkeley Professor J. Bokor's Chapter 7 course notes , shown below as an imgur image , on Temporal Coherence tonight. I am sending an email to Professor J. Bokor ...
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### Simple, physical explanations for Hadamard behaviour of two-point functions

The two-point function of local quantum fields on a curved spacetime exhibits a singularity of a very particular form, known as Hadamard form, for null separated points $(x,y)$ (including the ...
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### 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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### Why does correlation length diverge at the percolation threshold?

I'm reading a paper about electronic percolation. $p$ is the fraction of occupied bonds (or sites, depending on the model you're using, but I'll just use bonds), $p_c$ is the critical fraction of ...
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### S-matrix element

I'm confused with the relation between the fully resummed propagator in a given QFT and the corresponding S-matrix element. According to the LSZ reduction formula ($\phi^4$ theory for definiteness ...
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### How to measure the spin-spin correlation in a Monte Carlo simulation of the Ising model?

I'm simulating the Ising Model in 2D up to 5D and I want to calculate the spin-spin correlation, correlation length, and critical exponent of the system. What is a good way to go about doing this? ...
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### Why are Green Functions/(Correlation Functions) not on the mass shell?

The difference between Green Functions and the S-matrix in Quantum Field Theory is whether the momentum is on the mass shell. Why are the Green Functions/(Correlation Functions) not on the mass shell? ...
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### Correlation functions and connection to ward identities

I have the following definition of a general correlation function $$\langle \Phi(x_1)\dots \Phi(x_n)\rangle = \frac{1}{Z} \int [d\Phi] \Phi(x_1)\dots\Phi(x_n)e^{-S[\Phi]}$$ I have only just ...
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### Internal and spacetime symmetries?

I am trying to understand Wiki's explanation about correlation. Part of this article talks about internal and spacetime symteries: If the probability distribution has any target space symmetries, ...
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### Product of VEVs vs. VEV of product

How can we prove the following cluster decomposition formula $$\langle \phi_1 \phi_2 \rangle ~=~ \langle \phi_1 \rangle \langle \phi_2 \rangle,$$ where brackets denote vacuum expectation value (VEV) ...
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### Correlation Functions, Symmetries and Measurements

Is there a book that goes deep into correlation functions? What I'm interested in a book/article that explains in the detail the relation of the correlation functions with symmetries and how one can ...
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### Green's Functions from Gell-Mann and Low Theorem

What I want to do: $\newcommand{\ket}[1]{\left|#1\right\rangle}$ $\newcommand{\bra}[1]{\left\langle#1\right|}$ $\newcommand{\braket}[1]{\left\langle#1\right\rangle}$ The Gell-Mann Low Theorem tells ...
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### What's the difference between correlation functions and S-matrix, and between in-in formalism (or “closed time path formalism”) and in-out formalism?

I was reading the "in-in" formalism (or "closed time path formalism" used in condensed matter physics) in cosmology created by Schwinger in 1961, and there is a saying： "they care about correlation ...
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### 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 ...
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### S-matrix element for forward scattering and amputed green function

I'm studying dispersion relations applied as alternative method to perturbation theory from Weinberg's book (Vol.1) Let's consider the forward scattering in the lab frame of a massless boson of any ...
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### Pair correlation function of the QHE “plasma”

I am trying to teach myself the theory of quantum Hall effect, and realized that I can not reproduce a basic textbook result. Let me closely follow Girvin's Les Houches lectures (http://arxiv.org/abs/...
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### Autocorrelation function corresponding to density of states with significant rotational motion

Most statistical physics textbooks (at least the ones I've found) state simply that the density of states of a system can be found as the temporal Fourier transform of the velocity autocorrelation ...
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### 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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### Constructing Ward identity associated with conserved currents

Consider constructing the Ward identity associated with Lorentz invariance. It is possible to find a 3rd rank tensor $B^{\rho \mu \nu}$ antisymmetric in the first two indices, then the stress-energy ...
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### Why can we not reduce the size of a system below the correlation length without qualitatively changing its properties?

This question is posed in the context of thermodynamics/statistical mechanics. Suppose we define the correlation length as the $\xi$ in the exponential factor $e^{-r/\xi}$ that appears in the ...
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### Autocorrelation and Power density spectrum : Continuous Markov Process

I've been reading through the paper from Gillespie on Brownian motion and Johnson Noise (DOI, PDF). He considers $X_s(t)$, a zero-mean stochastic variable, that is stationary in the sense that all of ...
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### Autocorrelation Functions <---> Pair Correlation Functions

Are there any ways to convert an autocorrelation function to a pair correlation function, and vice versa?