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3
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0answers
96 views

Where does one find pair-correlation functions for various materials?

What is the canonical source for finding pair-correlation functions for atoms in various materials? I am interested in both numeric computations and experimental measurements (like might be obtained ...
3
votes
0answers
1k views

How to prove Wick's Theorem (Zee's eq. I.2 (16)) via Gaussian integration?

I'm working through Zee's QFT in a Nutshell but there's an integral [I.2 (16)] I couldn't quite derive. The problem is to find $$\langle x_i x_j ... x_k x_l\rangle=\frac{\int ... \int dx_1 ... dx_n ...
2
votes
1answer
225 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 ...
2
votes
1answer
54 views

What is meant by open-string tachyon scattering amplitude?

It was said here that Veneziano derived: open-string tachyon scattering amplitude from principles of Regge theory and S-matrix theory and used the Euler beta-function to make all the critical ...
2
votes
3answers
266 views

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 ...
2
votes
1answer
413 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? ...
2
votes
1answer
143 views

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? ...
2
votes
1answer
132 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
141 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
344 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
213 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
232 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
538 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
34 views

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 ...
2
votes
0answers
43 views

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 ...
2
votes
0answers
95 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
87 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
50 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
104 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
187 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
115 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
351 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
150 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
230 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
145 views

Finite temperature correlation functions in QFT

Suppose that we want to calculate this imaginary time-ordered correlation function for an interacting system (in Heisenberg picture) : $$\langle \mathscr{T} A(\tau_A)B(\tau_B) \rangle =\frac{1}{Z} ...
1
vote
3answers
63 views

Correlation function $\langle s_1(x, t)s_2(x', t')\rangle$ vs $\langle s_1(x, t)s_2(x', t')\rangle-\langle s_1(x, t)\rangle\langle s_2(x', t')\rangle$

The correlation function in statistical mechanics is defined in either of two ways $$g(\mathbf{x}-\mathbf{x}', t-t') = \left\langle s_1(\mathbf{x}, t)s_2(\mathbf{x}', t') \right\rangle$$ ...
1
vote
2answers
160 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
256 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
59 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
136 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
193 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
115 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
201 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
1answer
99 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
548 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 ...
1
vote
1answer
634 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
29 views

QFT: Limits in Time Ordered Correlation Function Derivation

Background In part of the derivation for the time ordered correlation function I have the following equation (This equation I am fine with - it is what follows that I am not), $$ ...
1
vote
0answers
37 views

Generating functional for free and interacting theories [closed]

I'm asking probably a stupid question. We define the generating functional for free theories as $$ Z_0[J] = \int D \psi e^{i\int d^4x \left[ L_0(x) + J_l(x)\psi^l(x) \right]} $$ with $L_0$ the free ...
1
vote
0answers
119 views

Proof of correlation function formula in quantum field theory

I am trying to prove the following formula used in QFT: $$\langle\Omega|T\{\Phi(x_1)\dots\Phi(x_n)\}|\Omega\rangle = \frac{\langle 0|T\{\Phi_I(x_1)\dots\Phi_I(x_n)S\}| 0 \rangle}{\langle 0|S| 0 ...
1
vote
0answers
48 views

Difference between the propagators and vertex function [closed]

I am confused between Green's function and vertex function in field theory. Can someone please explain the difference between the two in context ${\lambda} {\phi}^4$ theory?
1
vote
0answers
36 views

Solution of Dirichlet problem for scalar field in Ads

I am reading "Anti de Sitter space and holography" by Witten. In this article he derives the two-point function for CFT from theADS/CFT correspondence for a massless scalar field living in the bulk. ...
1
vote
1answer
26 views

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 ...
1
vote
0answers
32 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
18 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
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0answers
82 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
0answers
64 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
69 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
59 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
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0answers
43 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)\\ ...