# 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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### Symmetry of retarded R-current correlator in $\mathcal{N}=4$ Super Yang-Mills

The retarded correlator of the R-current $J_\mu$ of $\mathcal{N}=4$ Super Yang-Mills theory is $$C_{\mu\nu}(x-y)=-i\theta(x^0-y^0)\langle[J_\mu(x),J_\nu(y)]\rangle.$$ In this paper in eq. (2.4), I ...
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### Two Point Correlator

I have a problem to reproduce the following identity: \Pi_{\mu\nu}(q^2) = i \int d^Dx e^{iqx} \langle 0 | T \{j_\mu(x) j_\nu(0) \} | 0 \rangle = (q_\mu q_\nu - g_{\mu\nu} q^2 ) \...
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### Energy corresponding to the peak of velocity power spectrum

I ran a MD simulation for a number of N molecular hydrogen. I used the velocity time history of system for each atom and subtract the velocity of center of mass of each molecule from the velocity of ...
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### What are the 1PI correlations functions?

This question may be a little strange, but I'm currently going through my lecture notes and in the construction of the 1PI effective action there is a constant reference to 1PI correlation functions. ...
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### Estimation of the autocorrelation for data on finite size interval

Let's consider we have a continuous random signal ${ t \in ] - \infty \,;\, + \infty [ \mapsto b (t)}$. We assume this signal to be stationary, so that when ensemble-averaged, one may introduce the ...
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### What is the relation between scattering amplitudes, fluctuations, response functions and correlations in macroscopic equilibrium systems?

In Kardar's book Statistical Physics of Fields, he mentions that that correlations at different length scales can be measured by scattering. If its electric correlations, you would scatter light and ...
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### Why is the correlation of an observable and its derivative zero?

Why is the correlation of an observable and it's derivative zero? And why does this not only hold for $\langle A(t) \dot A(t) \rangle$ but also for $\langle A(0) \dot A(t) \rangle$ ? These averages ...
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### Why does decay of correlations imply absence of order?

In a few articles I have read, a two-point correlation function $\langle g(x)g(y) \rangle$ is shown to decay with increasing distance of $x$ and $y$, and this is then taken to imply an absence of the ...
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### Two definitions of Green's function

In literature, usually two types of definition exist for Green's function. $\hat{L}G=\delta(x-x')$. This equation states that Green's function is a solution to an ODE assuming the source is a delta ...
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### pair correlation function for heterogeneous nuclei

I have a system with heterogeneous size of nuclei of two liquids within a mixed fluid phase of those two liquids. I was wondering what would be the interpretation of pair correlation function for a ...
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I have read that not all correlated states are entangled. What is the difference between the two? Mathematically, it was stated that a system which can be put in the form of $\sum_{k}p_{k}\hat{\rho}... 1answer 262 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 ... 1answer 656 views ### Wick Contraction I am reading Quantum Field Theory in a Nutshell by A. Zee. Zee introduces the rationale/machinery behind Feynman diagrams in three steps: Baby -> Child -> "Real". The baby problem generates ... 0answers 66 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 $$... 2answers 320 views ### Transition amplitudes by functional methods in QFT I am following section 9.2 in Peskin and Schroeder in which the Feynman rules are derived for scalar fields. They define (in eqn (9.14), page 282) the transition amplitude from \vert\phi_a\rangle ... 3answers 189 views ### Proof for a time-ordering equation in Negele & Orland (1998) Let T be the time-ordering operator which orders operators A_1(t_1), A_2(t_2), \ldots such that the time parameter decreases from left to right:$$T[A_1(t_1) A_2(t_2)] = A_2(t_2) A_1(t_1) \text{ ... 0answers 54 views ### Non translation invariant correlator in CFT I'm doing an exercise on vertex operators in the CFT book by Di Francesco & al.; exercise 9.2 p.329 : Using mode expansion show that: $$\langle\tilde{\phi(z)}\tilde{\phi(w)}\rangle= - \text{ln} \... 1answer 932 views ### Why do disconnected diagrams not contribute to the S matrix? I've read somewhere that disconnected diagrams do not contribute to the S-matrix. I don't see why this is the case. I do know why vacuum bubbles do not contribute: given a generating functional for a ... 0answers 45 views ### Non Zero correlation function (for large separations) in one particle state? So i computed the following equal time correlation function for a one particle state. The vacuum correlations give the function$$\langle \phi(\vec x)\phi(\vec y)\rangle_0=D(\vec x-\vec y)\\ =\frac{e^{... 0answers 115 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 ... 0answers 260 views ### 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 ...
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 ...