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Questions tagged [correlation-functions]

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, instead.

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Bound on Quantum Chaos

I am currently reading the paper A Bound on Chaos. In this paper, they evaluate the quantity C(t), which is an out-of-time-order correlator (OTOC), and use very clever arguments to show that there ...
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How to understand complex masses of unstable particles? The conceptual problem of calculating decay rate

If a particle has a complex mass, $p^2-m^2=0$ leads to $p^μ \notin \mathbb R^4$. What does it mean? When you want to calculate S-matrix elements of decay process $\langle p_f,\ldots\mid p_i\rangle$, ...
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Tricky 3 particle distance correlation question for quantum mechanics

Three particles are detected/placed/focused at position $x=y=z=t=0$. (So that according to quantum mechanics their momentum/energy are completely unknown). They are non-interacting Fermions each with ...
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Faddeev-Popov determinant and topology of the wordline

I am studying the path integral quantization of relativistic particles, using the BRST quantization method. I have to compute the integral \begin{equation} Z\sim \int Dx \det(\partial_\tau)e^{-\int_0^...
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How to understand the two-point correlation function in momentum space?

Let's take the Ising model as an example and study the two point spin spin correlation function: $$\langle s_0 s_r\rangle = \frac{\sum_{\{s_i\}}e^{K\sum_{\langle i ,j\rangle}s_i s_j} s_0 s_r}{\sum_{\{...
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A puzzle about Green's function and S-matrix

From the discussion in some posts example1, example2, we know that the S-matrix is the residue of the corresponding Green's function. On the other hand, S-matix is a physical observable in QFT, but ...
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Expectation value of a path-ordered exponential

Let us define our path-ordered operator $\overrightarrow{U}\left(t_1,t_2\right)$: $$ \overrightarrow{U}\left(t_1,t_2\right)=\overrightarrow{\mathcal{P}}\exp\int_{t_1}^{t_2}dt\,\mathcal{O}\left(t\...
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Closed set of operators under renormalization

While reading the article http://inspirehep.net/record/61135, I came across the concept of "closed set under renormalization". The definition they give is the following. In any renormalizable field ...
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Deriving Ward identity directly from a given formula for the conserved current only using the equal-time canonical commutation relation

I have a very technical question on deriving a Ward identity directly from a given explicit form of the "conserved current". Let me emphasize that I do not start with an apriori knowledge on the ...
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Constraints on correlation functions of Quasi Primary Fields

I have problems understanding constraints on correlation functions of quasi primary fields (QPF) following DiFrancesco's Conformal field theory book. In chapter 4, section 4.2.1, a QFP is defined as a ...
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Symmetry factor in $\phi^4$ theory

I'm having trouble while trying to understand what the symmetry factor of a Feynman diagram really is. From books I get that it is a geometrical factor that you get by the number of ways in which you ...
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Feynman Rules for Two Different Interacting Fields

I'm currently studying how to deduce Feynman rules for general theories, and I've managed to deduce them for $\phi^3$ and $\phi^4$ theories. Up to this point I've considered the same field for all ...
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Finding the correlation function using the expression of the free energy (Ising model, Landau theory)

I am working on a homework problem regarding the Lee Yang theorem, though my issue already exist using only the standard approach to the Ising model. Simply put, i have no idea how to explicitly ...
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Electron correlation - difference between correlation and dependence

When we talk about electron correlation in condensed matter physics or chemical physics, we usually refer to the fact that the pair-density $$ P(r,r') = N(N-1) \int |\psi(r,r',r_3,...,r_N)|^2 \; \...
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Obtaining real-space correlations from reciprocal space correlations

Consider a system of Ising variable $s = \pm 1$ on a rectangular lattice which has open boundary conditions on the top and bottom and periodic boundary conditions to the left and right. In other words,...
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How to calculate correlation functions for fermionic operators?

In the paper by Peschel (2003) https://arxiv.org/pdf/cond-mat/0212631.pdf How does one derive the following relation: $$ \langle c_{n}^\dagger c_{m}^\dagger c_{k}c_{l}\rangle = \langle c_{n}^\...
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Kosterlitz-Thouless transition and correlation function

I’m studying Kosterlitz transition on this book: https://tinymachines.weebly.com/uploads/5/1/8/8/51885267/kardar._statistical_physics_of_fields__2007_.pdf#page173 . At page 165 it says:” The gradient ...
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Spin spin correlation function in topological phase transition?

during my vacation i have decided to study Kosterlitz and thouless phase transition (i have already posted 2-3 questions about that). I don't know quantum field so I did not expect to understand ...
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What is the link between statistical and QFT correlation functions?

I'm studying statistical mechanics in particular correlation function: https://en.wikipedia.org/wiki/Correlation_function_(statistical_mechanics) and I have understood it. Now searching on internet ...
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Simple reason why the correlator of a vector with two identical scalars vanishes?

In scalar QED, the photon interacts with a charged scalar and the three point function of a vector, scalar and scalar bar is nonzero. I remember an argument that very simply proved that if you try ...
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Brownian motion from two gaussian noise processes

Consider some brownian motion for which we obtained the following solution for the langevin equations $$ u\left(t\right)=e^{-\alpha t}\int_{0}^{t}e^{\alpha s}\left(\xi\left(s\right)-\xi'\left(s\right)...
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Truncated $N$-Point Functions

In Quantum Field Theory, truncated N-Point functions (or truncated Green's functions) are the N-Point functions of diagrams with their external legs chopped off. I was told that the truncated N-Point ...
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How can a Dirac delta function that does not occur under an integral be used to describe a transition rate?

In his excellent notes (found here), Mark Tuckerman shows that the transition rate of absorption between quantum states i and f, coupled by operator B, can be expressed as the fourier transform of the ...
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Density density correlations of a simple Brownian particle [closed]

Suppose, I have a particle satisfying the equation \begin{equation} \frac{dX}{dt}=\eta(t) \end{equation} Where $\langle \eta(t)\eta(t')\rangle=\delta(t-t')$. I can now define a density like $\rho(x,...
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One-point correlation function of any quasi-primary operator is zero

How do I show the following: In a general CFT (with no boundary), the one-point correlation function of any primary operator $A_Δ$ is $0$ (unless we are talking about the identity operator): $$<...
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Equipartition and correlations

This question references C.L.Henley's paper on arxiv. Page 3, section B: Effective free energy and correlations. There is an ice polarization field $\mathbf{P}(\mathbf{r})$, that has been coarse ...
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Two Time Correlation function calculated from Born rule

Update Below I'm having a hard time reconciling two different calculations of the quantum two time correlation function. Consider quantum operator $A$ with eigenvectors $\{|\phi_i\rangle\}$ and ...
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Is there any difference between radial distribution function and pair correlation function?

I have understood the part that for solids pair correlation function is the measure of the probability of finding the center of another particle in the neighborhood of a given particle. On the other ...
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Current-current correlator in superconductivity

I was reading a paper on superconductivity. There is a claim that if the momentum space current-current correlation function $\langle\mathcal{T} j_{\mu}(k)j_{\nu}(-k) \rangle$ has a pole at zero ...
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What's The 2pt Correlation Function For The Spin Fields For The 3D Critical Ising Model?

The title it self explanatory. What's The 2pt Correlation Function For The Spin Fields For The 3D Ising Model? I know the form of the four point function and have worked out how to express it in terms ...
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statistical errors associated to Monte Carlo sampling

I have $n$ successive observation $A_\mu $ of a quantity $A$ and I need to understand how the expectation values of the square of the statistical error depends from the autocorrelation time but a ...
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correlation function in Fourier space

I'm reading this paper and want to prove eq (8): The field $\psi(\mathbf{x}) \in \mathbb{C}$ exists in a finite periodic 2D square box (of side length $L$), and has a Fourier series expansion, and ...
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“Contraction Property of thermal density matrix” in the Maldacena's paper of A Bound of Chaos

In the paper, https://arxiv.org/abs/1503.01409 (Maldacena, et al. “A Bound on Chaos.”) in equation (24), the authors write an inequality, $$ Tr( y^{1+\eta} V y^{3-\eta} V ) \leq Tr(y V y^2 V) $$Where $...
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How to understand that correlators measure physical correlation?

Background In physics, we always come across $n$-point correlators (e.g. 2-point correlators). For instance, in phase transitions, one is interested in finding the correlation function between order ...
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Help with Correlation/Green's Function of Rotated Variables (Keldysh Rotation)

I'm working through this paper, and have encountered "a little algebra shows that...", yet I'm not familiar enough with the topic at hand to figure this out. Here is the paper: https://arxiv.org/abs/...
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Shear strain correlations from displacement Fourier transform

Currently working with molecular dynamics simulations, I would like to compute shear strain correlations in my 2-dimensional system. How I used to do things Accumulated shear strain at position $\...
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Are correlation functions in CFTs always single-valued functions?

I am wondering whether correlation functions e.g. in 2D CFTs such as $$\langle \phi\phi\phi\rangle=C\frac{1}{z_{12}^{h_1+h_2-h_3}z_{23}^{h_2+h_3-h_1}z_{31}^{h_3+h_1-h_2}}\frac{1}{\bar z_{12}^{\bar ...
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Simplifying CMB correlation function with spherical harmonics

I originally asked this on the physics Stack Exchange site, but perhaps it could be more easily answered here. Given the definition of the correlation function for CMB temperature fluctuations as $$ ...
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How are correlation length and cluster size related in the 2D Ising model?

What is the relationship between correlation length and cluster size? Does the correlation length give the average cluster size, or is the cluster size something different?
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Scattering in $g\phi^3$-Theory

I have to consider the QFT with the Lagrangian $$\mathscr{L}=\underbrace{\frac{1}{2}\partial_\mu \phi \partial^\mu \phi - \frac{m^2}{2}\phi^2}_{=\mathscr{L}_0}\underbrace{-\frac{g}{6}\phi^3}_{\...
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Correlation length

I am working with the spin-1/2 quantum antiferromagnet Heisenberg model. I have found literature about the correlation length of this model for 2D. However, what would it be in 1D? I have the ...
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Is the thermal expectation value of a square of Hermitian operator always finite?

If $\mathcal{O}$ is an hermitian operator in a system given by Hamiltonian $H$ and inverse temperature $\beta$, is $$\langle \mathcal{O} \mathcal{O} \rangle = Tr (e^{-\beta H} \mathcal{O} \mathcal{O})...
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Making use of functionals in Martin Siggia Rose formalism

I am currently studying "Critical Dynamics - A Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior", and came across an issue I can't solve. If you know about functional ...
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What is the interpretation of $n$-point Green's functions, for $n>2$?

Disclaimer: I am not a Physicist. So please correct any misunderstanding that I may have. From what I understand, a $2$-point Green function can be interpreted as the response at $x_2$, when you have ...
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Ginzburg Criterion - for mean field theory vs for Gaussain approximation

It is often stated that the Ginzburg criterion for mean field theory and the Gaussian approximation are the same. Goldenfeld, 1992; pg$\sim$170 tries to show the Ginzburg criterion for mean field ...
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Unusual Feynman Integrals at Two-Loops

I'm studying a very particular conformal field theory where unusual Feynman integrals appear when I'm trying to evaluate a two-loop correlator (in position space). These integrals are on the form $\...
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First order correlation function - Simple example

I am trying to figure out whether the superposition of two stable monochromatic waves is coherent everywhere, and while I expect that to be the case my calculation doesn't show that to be always true. ...
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Ginzburg Criterion - why average over the Correlation Length?

To derive the Ginzburg criterion for the upper-critical dimension the fluctuations are averaged over a volume set by the correlation length. Why is this done? i.e. why do we average over a volume in ...
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LSZ reduction formula derivation

I am following the derivation of the LSZ reduction formula on Weigand's notes. We arrive at eq. 2.64, schematically \begin{equation} \tag{1} \label{LSZ} \langle p_n, \text{out}|q_r, \text{in}\...
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Path-Integral of Charged Particle in Chern-Simons Gauge Fields

From the paper "Fermi-Bose Transmutations Induced by Gauge Fields" by Polyakov, http://inspirehep.net/record/22956 http://dx.doi.org/10.1142/S0217732388000398 the theory in 3D, $$\mathcal{L}=\sum_{...