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2
votes
1answer
105 views

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, ...
2
votes
1answer
135 views

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) ...
2
votes
2answers
327 views

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 ...
2
votes
1answer
104 views

Regarding a small step in the derivation of the LSZ formula

I'd like to prove the LSZ formula, but there is a specific step that is bugging me a lot. I know there are many subtleties in its derivation, but I'm not worrying about this right now: I'm trying to ...
2
votes
1answer
143 views

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 ...
2
votes
1answer
177 views

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 ...
2
votes
2answers
490 views

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 ...
2
votes
0answers
39 views

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 ...
2
votes
1answer
70 views

Computation of the QCD vector two point function

I am following some notes on the computation of the vector two point function in QCD and I would like somebody to make some intermediate steps more explicit. Let's consider ...
2
votes
0answers
44 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} ...
2
votes
0answers
88 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 ...
2
votes
0answers
106 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 ...
2
votes
0answers
100 views

Is time ordering defined for a single operator depending of two time variables?

The time ordering for the purpose of quantum mechanics is e.g. given by $${\mathcal T} \left[A(x) B(y)\right] := \begin{matrix} A(x) B(y) & \textrm{ if } & x_0 > y_0 \\ \pm B(y)A(x) & ...
2
votes
1answer
336 views

How exactly do I calculate this correlation function?

I found a research paper (from 1977) that has a particular equation I need to reproduce. The paper essential calculates dynamic light scattering correlation functions. The full equations I need to ...
2
votes
1answer
145 views

Eigenvalues of a mean correlation matrix (integral over correlation matrices with arbitrary density)

Consider a stationary dynamic system with state $s(t)$ and correlation structure described by $C_{ij}(\tau)=\mathbb{E}[(s_i(t+\tau)-\bar{s_i})(s_j(t)-\bar{s_j})]$. Given an arbitrary density function ...
2
votes
0answers
195 views

How does one derive the 2 halo term in two-point correlation function

This question is in reference to the paper here. In Equation (86) on page 28, the authors have given the two point correlation function \begin{equation*} \xi(\mathbf{x}-\mathbf{x}^{\prime}) = ...
1
vote
2answers
155 views

$\langle B|A \rangle$ expressed in terms of the Partition Function

Say you have an electron departing from point A and reaching poing B after a time t. According to some helping friend, the Partition Function for that electron going from point A to B can be written ...
1
vote
2answers
200 views

Vacuum to vacuum transition amplitude using functional integral

The vacuum to vacuum transition amplitude for a free particle with source $J$ is given by $$Z_0[J]=\int D\phi \mathrm{exp}\{-i\int [\frac{1}{2}\phi(\square +m^2-i\epsilon)\phi-\phi J]d^4x\}$$ Let ...
1
vote
2answers
40 views

Does the connected Green's function's decomposition into 1PI-s have connected contributions, or can it be written exclusively using 1PI-s?

While reading this article by Abbot on the background field method, in Fig 5. on page 38 (page 6 in the pdf file), we can see the relation between connected contributions to the two point function and ...
1
vote
1answer
126 views

Lightcone singularity of a 3 point function in CFT

I had a quick question regarding the title of the question. In e.g. 2D CFT (for simplicity), the three point function of three operators with conformal dimension $a$, $b$ and $c$ are given as $$ ...
1
vote
1answer
182 views

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 ...
1
vote
1answer
87 views

Correlation function and scattering amplitude in critical phenomena

When we use scattering radiation to probe critical phenomena, we have the usual Bragg relation for constructive interference $$|\vec{k}|=\frac{4\pi}{\lambda}sin\frac{\theta}{2}$$ where $\vec{k}$ is ...
1
vote
1answer
219 views

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? ...
1
vote
1answer
74 views

Why do we have different signs before the delta on the Klein-Gordon and the Dirac Green's function equation?

Let's read equation (2.56) on Peskin & Schroeder $$(\partial^2+m^2)D_R(x-y)=-i\delta^4(x-y).$$ Let's look now to equation (3.118) $$(i\gamma^{\nu}\partial_{\nu}-m)S_R(x-y)=i\delta^4(x-y).$$ ...
1
vote
1answer
539 views

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 ...
1
vote
1answer
1k views

Autocorrelation Functions <---> Pair Correlation Functions

Are there any ways to convert an autocorrelation function to a pair correlation function, and vice versa?
1
vote
0answers
13 views

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 ...
1
vote
0answers
14 views

Are correlators constructed out of Wilson loops singular in pure Yang-Mills?

If I have some gauge invariant function of two Wilson loops (such as $\left<\text{Tr}W_1 \text{Tr}W_2\right>$) does the expectation value diverge when the loops coincide the same way ...
1
vote
0answers
70 views

Wick's Theorem For Product of Fields [closed]

I am trying to write an expression for $$\langle (\phi(x,t))^m (\phi(x',t'))^n \rangle$$ where $n$ and $m$ are even with respect to a real Gaussian action, in terms of $$\langle \phi(x,t) ...
1
vote
1answer
111 views

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 ...
1
vote
0answers
40 views

Correlation time (non linear) in ising model (3D)

I am currently implementing the classical Ising model (3D) for a demonstration. I use the common implementation of metropolis,teller,teller ("Metropolis"-algorithm) and measure certain quantities. ...
1
vote
0answers
51 views

How to calculate the correlation function for a discrete series of data [closed]

Using a simulation, I have generated a random field, which is basically a list of complex numbers. How do I calculate the correlation function of the field? To be more specific: which are the ...
1
vote
0answers
53 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 $$ ...
1
vote
0answers
29 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)\\ ...
1
vote
0answers
92 views

Derivation of Higher-order correlation functions from definition

I'm trying to understand the definition of the n-th order correlation function. My aim is to translate the math into a numerical implementation in order to compute the correlation function $g^{(n)}$ ...
1
vote
0answers
184 views

Equal time displacement correlation functions and their physical interpretation?

Displacement correlation functions in question are within harmonic approximation and are derived for example in: A. Maradudin, Dynamical properties of solids 1, 1 (1974). Maradudin says about the ...
0
votes
1answer
551 views

Confusion with LSZ reduction formula

LSZ reduction formula relates the matrix element of the scattering operator to the n-point Green's function $$\langle 0|\phi(x_1)\phi(x_2)...\phi(x_n)|0\rangle$$ My question is: Is the vacuum on the ...
0
votes
1answer
260 views

Applying theorem of residues to a fermionic reservoir correlation function in order to solve the integral in the CF and obtain a summation

Applying theorem of residues to a fermionic reservoir correlation function in order to solve the integral in the correlation function and obtain a summation.
0
votes
1answer
58 views

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 ...
0
votes
1answer
183 views

What does a correlation function measure and how does it do this mathematically?

I would really appreciate if someone could explain. What does a correlation function like a density-density correlation function $$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$ ...
0
votes
1answer
734 views

Is there a difference between correlation processing and matched filter processing?

Is there a difference between correlation processing and matched filter processing? To me, they look same.
0
votes
1answer
164 views

Two point function for massless boson in 2 dimension

Is it true that two point function for massless boson theory in 2 dimension is a constant? That is to say it is independent of the distance between the two points?
0
votes
0answers
11 views

Correlation Function of Langevin Equation

Suppose $\phi(x,t)$ is a function whose dynamics are governed by a Langevin equation. We may Fourier transform to obtain a Langevin equation for $\phi(q,t)$. Is it true in general that $ \langle ...
0
votes
0answers
58 views

Ising Model 2D Correlation Length

I'm using Metropolis and Wolff Clustering algorithms to estimate the spin-spin correlation function $$<s_os_r>$$ I know that this is related to the correlation length but how do we determine ...
0
votes
0answers
48 views

Measuring typical distance between patches using 2D Fourier Transform

I need to extract information about the typical distance between the black patches in an image like the one I attached here. I tried to perform 2D FFT on it (using OpenCF fdt function in Python), but ...
0
votes
1answer
82 views

What's the meaning of the propagator in QM?

Yesterday I was solving some exercises, and after solving the time evolution I was asked to find the probability of the system to some state. In specific: $$|\Psi(t)\rangle = ...
0
votes
0answers
23 views

Ising Monte-Carlo and Three point functions

I'm looking for literature on the calculation of three points function in the 2d Ising Model using numerical methods, especially around the critical point. By $Z_2$ symmetry, three spin insertions is ...
0
votes
0answers
45 views

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 ...
0
votes
1answer
386 views

Green function for simple harmonic oscillator

I'm interested in examples on how to use Green function (GF)for simple harmonic oscillator (SHO)? I am from undergrad physics, so I need a fundamental math and quantum mechanical application of GF ...