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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Hartree-Fock factorization

I am studying c-field methods applied to Bose-Einstein condensates to understand how one gets to e.g. the dissipative GPE. To do so, one splits the field operator for the Bose gas into a low- and a ...
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Time dependence of Drude-like correlation function obtained from Matsubara formalism

I'm trying to calculate the real time dependence of the correlation function that I've obtained in my effective model (it is closely related to the electron density correlation function), given in ...
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Computing correlation function $\langle e^{i\beta \phi(x)}e^{-i\beta\phi(0)}\rangle$ for massless scalar field $\phi$

I am currently reading Shankar's "Bosonization: How to make it work for you in condensed matter" (http://inspirehep.net/record/408901/). In page 9, I am stuck with computing the correlation function ...
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How to prove that a given correlation function is protected?

I would be interested in proving that $2$-point functions made of $1/2$-BPS operators are protected in $\mathcal{N}=4$ SYM (Supersymmetric Yang-Mills), i.e. that the correlator $\langle \mathcal{O}_2(...
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Significance of LSZ reduction formula

LSZ reduction formula relates the S-matrix element and the time-ordered correlation function, in a complicated equation. However, since $$S=T e^{-i\int d^4x H_I}$$ where $H_I$ is the interaction ...
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Quantum and classical correlation functions [duplicate]

Are quantum and classical correlation functions the same? To the best of my knowing they are derived differently. But when people speaks about correlation functions they always refer to the classical ...
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Is there a general behavior of energy gap under renormalization?

Perform real space renormalization on a discrete lattice model with a finite energy gap. Is it always true that under the flow of coarse-graining, the energy gap will only increase? I think the ...
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Local fields vs particles

I have heard it said that Richard Feynman was a proponent of a particle approach to QFT while Julian Schwinger preferred a local fields description. What is meant by “local fields”? Surely when one ...
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Correlation functions of quantum Ising models

I have a single technical question regarding a statement on page 7 of the paper "Dynamical quantum correlations of Ising models on an arbitrary lattice and their resilience to decoherence". The paper ...
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Spatial Correlation Function and Ensemble average

Well, I was reading the Statistical Mechanics book by Pathria, to understand the concepts of the correlation function. I want to quote some lines. Spatial correlation functions are based on n-...
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How to properly make sense of the $\mathcal{S}$-matrix as a correlator on a sphere?

In the book "Lectures on the Infrared Structure of Gravity and Gauge Theories" by Andrew Strominger, the author discusses in Chapter 3 the idea of "The $\mathcal{S}$-matrix as a Celestial Correlator". ...
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In 2D CFTs what are the possible forms of correlation functions

I am following Sylvain Ribault's lectures on 2D CFT (https://arxiv.org/abs/1609.09523) in which he lays out 2D CFTs in an axiomatic format. In a CFT we assert (as an axiom) that there is a ...
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OPE coefficients of primaries in a 2D CFT

I am trying to compute the OPE coefficients in a 2D CFT, and I am convincing myself of something that I know is not true but cant find my mistake. Given primaries $V_{\Delta_1}$ and $V_{\Delta_2}$ I ...
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Correlation function calculation

From Mehran Kardar's Statistical Physics of Fields page 38 section 3.2 [...] $I_d(x,\xi)$ is the solution to the following differential equation $ \nabla^2 I_d(x) = \delta^d(x)+ I_d(x)/\xi^2$ ...
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Calculation of 3-point function given a generating funcional $Z[J]$

With: $$\ln Z[J]= \int dt \frac{J^2(t)}{2} f(t) + C \int dt \frac{J^3(t)}{3!}$$ I am asked to calculate the 3-point funcion. Attempted solution: The 3-point funcion is given by $\frac{ \delta^3 }{\...
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Upper bound for norm of 1-body correlation tensor of qubit

Any $n$-qubit state can be expressed as $$\rho=\frac{1}{2^{n}} \sum_{\mu_{1}, \ldots, \mu_{n}=0,1,2,3} T_{\mu_{1}, \ldots, \mu_{n}} \sigma_{\mu_{1}} \otimes \ldots \otimes \sigma_{\mu_{n}}$$ where $...
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Correlation length anisotropy in the 2D Ising model

In the Ising model, the two-spin correlation function is $$ C(\vec{r}) = \langle \sigma_{\vec{r}_0+\vec{r}}\sigma_{\vec{r}_0}\rangle - \langle \sigma_{\vec{r}_0+\vec{r}}\rangle \langle \sigma_{\vec{r}...
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Large $c$ limit and connected correlation functions in $2d$ QFT

EDIT: This question has been edited thanks to a comment. One of my definitions was wrong, so I have rewritten the whole question. I was reading this paper about $T \bar{T}$ deformations of $2d$-QFTs ...
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Why has the free boson a charge $c=1$ in 2D CFT?

In the free scalar field theory in 2D conformal field theory, we consider the correlation functions of the derivatives of the fields, i.e. $$\langle \partial \phi(z) \partial \phi(w) \rangle, \tag{1}$...
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Correlation function of partition functions

In this paper the authors study the correlation function of partition functions defined by $$\langle Z(\beta_1) \ldots Z(\beta_n) \rangle = \frac{1}{\mathcal{Z}}\int \mathrm{d}H \, \mathrm{e}^{-L \, \...
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Question on the correlation function of dichotomous Markov noise

Setup: A two-state switching process $I(t)$ between two values $\Delta_1$ and $\Delta_2$ with rates $\alpha$ and $\beta$ can be represented by the transition probabilities $$ P_{ij}(t) = \frac{1}{\...
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Correlation function from Laplace transform of distribution function?

I have a time-dependent random process $x(t)$ which takes on two values $\Delta_1$ and $\Delta_2$. I know the Laplace transforms of the (time-dependent) probabilities $\hat{p}_{ij}(s)$ of these values ...
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Signal coherence/correlation vs quantum coherence

In general, I understand a signal $s(t) \in \mathbb{C}$ is called "coherent" when it has a large autocorrelation function. A pair of different signals $s(t)$, $r(t)$ can also be "coherent" if their ...
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Do Bell’s inequalities assume particles can only have one variable to consider?

I have asked the question “How do you know when pairs are entangled?” I have asked “What is the difference between entangled and correlated?” I have also asked several similar questions, but I keep ...
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How to deduce the formula of the Correlation Length on a periodic lattice?

Sometimes in Monte Carlo simulations we need to compute the correlation length, but this is a hard task without a formula. However, for instance, in an periodic cubic lattice of $L^3$ spins, some ...
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Scattering amplitudes vs correlators

What are the practical differences between correlators and scattering amplitudes in quantum field theory? On a very practical level: scattering amplitudes describe the evolution of an IN state into ...
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A question in imaginary time Green's function

I am learning many-body quantum field theory with Bruus and Flensberg's Introduction to Many-body Quantum Theory in Condensed Matter Physics, there is a derivation that confuses me a lot. To add ...
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Veneziano amplitude from 3-point constants

Consider an open bosonic string in the critical dimension at $g_s = 0$ (only the sphere contributes to the string amplitude). The scattering of 4 tachyons is given by the Veneziano amplitude. I'm ...
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Systematic way of calculating 3-point worldsheet amplitudes

I'm looking for a systematic way of deriving the 3-point functions $\left< V_1(z_1, \bar{z}_1) V_2(z_2, \bar{z}_2)V_3(z_3, \bar{z}_3)\right>$ of the worldsheet CFT of a closed bosonic string. ...
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Vanishing correlation function

Mirror Symmetry p. 206, Eq. 10.192. I have an operator $\mathcal{O}$ that commutes with my supercharge $\overline{Q}_+ $, $\left[\overline{Q}_+, \mathcal{O} \right]=0$. Why does the correlation ...
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How to derive equation (N.15) in Ashcroft and Mermin's Solid State Physics?

They state in their book on page 792 the following: It can be proved, however, that if $A$ and $B$ are operators linear in the $u(R)$ and $P(R)$ of a harmonic crystal, then: $$\langle e^A e^B \...
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Correlation function at zero distance

I'm confused about the definition of the correlation function (at equal time). I know it is defined from the thermal average of the scalar product of two random variables (for example the spins of a ...
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Does somebody know where to find original paper of Lehmann, Symanzik and Zimmerman translated in English?

does anybody know where to find original paper about LSZ reduction translated in english? unfortunantely, Ive found only original German article. H. Lehmann, K. Symanzik, and W. Zimmerman, "Zur ...
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Spinwaves, Mermin-Wagner theorem, Two-point correlation function and Heisenberg model

I was looking at the Mermin-Wagner theorem (as following the previous question) and the Heisenberg model seems to be presented, and they split the Hamiltonian $H$ in the matrix or vector n-components ...
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Expectation value of descendant fields

I'm trying to calculate the following quantity: $ \left<(L_{-1}\phi)(w_1)(L_{-1}\phi)(w_2) \ldots (L_{-1}\phi)(w_N) \right>$ where $\phi(w_i)$ is a primary operator and $L_{-1}$ is the ...
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Quantum field theory: corrections to excited state correlation functions

I want to know how to calculate the lowest-order-in-the-coupling-constant correction to $$M(x, y,k,p)=\langle k|\phi(x)\phi(y)|p\rangle$$ in $\phi^4$ scalar field theory in a relatively general ...
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Asymptotic LSZ reduction formula (Peskin & Schroeder)

Peskin & Schroeder, An Introduction to Quantum Field Theory, write at page 224 $$\int d^{4} x e^{i p \cdot x}\left\langle\Omega\left|T\left\{\phi(x) \phi\left(z_{1}\right) \cdots\right\}\right| ...
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Relation between standard and Kubo-transformed quantum correlations

Via path integral molecular dynamics it is possible to measure the Kubo transformed correlation function between two operators $\hat A$ and $\hat B$ \begin{equation*} K_{\hat A\hat B} = \frac 1 {Z_\...
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How do I fit a resonance curve?

In an experiment, I collected data points $ (ω,υ(ω))$ that are modeled by the equation: $$ υ(ω)=\frac{ωC}{\sqrt{(ω^2-ω_0^2)^2+γ^2ω^2}} \,.$$ How can do I fit the data to the above correlation? And ...
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Linear response treatment of the magnetization of a system of noninteracting fermions

While trying to solve an exercise, I ran into what looks like a contradiction. I'm sure I'm making some kind of mistake, but I couldn't spot it. I'm not asking for help in solving the exercise, which ...
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Error in histogram measurements

I ran into the following statement here and here but I believe it's more general. Let's suppose we're running a simulation of a system and we are interested in the distribution of a quantity (say $M$...
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Calculation of current from path integral

I would like to calculate $\langle\bar{\psi}\psi\rangle$ in free theory. I start from the following generating functional: $$Z[J]=\int\mathcal{D}[\bar{\psi},\,\psi]\exp\left(i\int d^dx\,[\bar{\psi}(i\...
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Two-point correlation function of a scalar field $\langle 0 | \phi(x) \phi(0)| 0 \rangle$

I'm trying to find the two point correlation function for a massless scalar field obeying $\square \phi = 0$. I can write $$\langle 0 | \phi(x) \phi(0)| 0 \rangle = \int \frac{d^dk}{(2\pi)^d} \delta(...
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Assumptions behind Ornstein-Zernike correlation function

Let $S(\mathbf q)$ be come correlation function in Fourier space ($\mathbf q$ = wavevector). In the study of condensed matter systems, I have often encountered the statements that a reasonable form ...
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Four point function with complex momenta?

It is well known that the four-point function $$\int_{\mathbb{R}^{3,1}}\frac {d^4 q}{((q+p_1)^2-i\epsilon)((q+p_2)^2-i\epsilon)((q+p_3)^2-i\epsilon)((q+p_4)^2-i\epsilon)}$$ can be computed using the ...
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What does Lorentz index structure say about a full-fledged correlator?

I have a probably dumb question. Consider the following position space correlation function in a YM-theory (with or without matter fields): $$f_{\mu_1\cdots \mu_n}^{a_1\cdots a_n}(x_1,\ldots,x_n)=\...
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Simple explanation of a particular diagrams of Feynman [closed]

In relation to this question posed on the website TeX.SE. I am curious to know the use in Physics of green functions about the signs of feynman diagrams with fermionic fields. I have not understood ...
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Bond order correlation function

I am trying to compute the bond order correlation function, $g_6$. It is defined based on the bond order parameter: $$\psi_6(x_i) = \frac{1}{N_i}\sum_{i=1}^{N_i}{\exp(i6\theta_i^j)}$$ where $\theta_i^...
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Different Schwinger-Dyson Equations

In the literature on QFT there are a lot of different equations that are all called "Schwinger-Dyson equation" so I wanted to know how are they related and if they have proper names. The first ...
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What substitutions are allowed within time-ordered products?

I always thought of the time-ordering in QFTs as an explicit operation. Meaning the time-ordering "operator" just takes everything I write inside it and shuffles the operators around until they are in ...