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18 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 ...
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1answer
61 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) $$(i\gamma^{\nu}\partial_{\nu}-m)S_R(x-y)=i\delta^4(x-y).$$ ...
2
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2answers
34 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 ...
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2answers
72 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 ...
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1answer
118 views

What is the difference between correlation and entanglement?

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 ...
1
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1answer
93 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 ...
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0answers
26 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 ...
3
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1answer
196 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 ...
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0answers
41 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 $$ ...
0
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1answer
117 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 ...
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0answers
111 views

LSZ reduction vs adiabatic hypothesis in perburbative calculation of interacting fields

As far as I know, there are two ways of constructing the computational rules in perturbative field theory. The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free ...
3
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2answers
152 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 $\vert\phi_a\rangle$ ...
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0answers
38 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} ...
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0answers
17 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)\\ ...
2
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0answers
54 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
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0answers
75 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 ...
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0answers
80 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 ...
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1answer
121 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 ...
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0answers
49 views

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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1answer
59 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.
1
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0answers
56 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 $g^{(n)}$ ...
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0answers
60 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: ...
3
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1answer
160 views

Quantum Field Theory without LSZ, how is it possible?

Most modern texts spend some time deriving the LSZ reduction formula that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you ...
3
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2answers
88 views

Three-body correlation function in kinetic theory

In Kinetic Theory, one studies the evolution of a system of $N$ particles interacting with each other. We use the notation $\boldsymbol{w}_{i}$ to describe the coordinates in phase-space of each ...
3
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1answer
91 views

Autocorrelation of noise - negative correlation

I am investigating autocorrelation of electrical noise as part of an undergraduate experiment (as detailed in http://physlab.lums.edu.pk/images/a/ab/Correlation.pdf). I sampled noise voltages using an ...
2
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1answer
74 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, ...
0
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1answer
330 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 ...
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0answers
53 views

What is the physical meaning of the “projection” of the mutual intensity function of a given signal?

Let's consider an optical wave $$\psi(t) = \psi(t, x=0)$$ Its mutual intensity function is defined as : $$ \gamma(t,\theta) := \psi(t+\theta/2).\psi(t-\theta/2) $$ So, what is the physical meaning of ...
3
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1answer
110 views

Equation 7.22 in Peskin & Schroeder: writing the Fourier transform of a two-point function as a series of 1PI diagrams

In Peskin and Schroeder's QFT book, on page 219, there is the following equation: The heading to the equation is: "The Fourier transform of the two-point function can now be written as". Could ...
4
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1answer
145 views

To what extent correlation functions determines the theory (and lagranian)

In other words, does a finite set correlation functions sufficient to determine a theory? Is there a chance correlation functions are more fundamental then the lagrangian?
2
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3answers
116 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{ ...
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2answers
149 views

What is the sense of introducing generating functional to the summands of expansion of S-matrix?

Let's have generating functional $Z(J)$: $$ Z(J) = \langle 0|\hat {T}e^{i \int d^{4}x (L_{Int}(\varphi (x)) + J(x) \varphi (x))}|0 \rangle , \qquad (1) $$ where $J(x)$ is the functional argument ...
4
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3answers
343 views

Applying theorem of residues to a correlation function where the Fermi function has no poles

Let $n_F(\omega) = \large \frac{1}{e^{\beta (\omega)} + 1}$ be the Fermi function. A fermionic reservoir correlation function is given by: $$C_{12}(t) = \int_{-\infty}^{+\infty} d\omega~ ...
4
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0answers
80 views

Can the correlation for the Potts model be bounded?

I am studying a $d$-state Potts model. A configuration $\sigma$, which assigns for each $x\in \mathbb{Z}^2$ a value $\sigma(x)\in [1,2,\ldots,d]$, with the probability on a finite lattice defined as ...
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1answer
226 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.
1
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1answer
111 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 $$ ...
2
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0answers
80 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) & ...
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2answers
384 views

“Correlation energy” using the pair correlation function

In this paper on the Quantum Hall effect the authors refer to something called the correlation energy of electrons. It is defined at the top of page 5 as $E=\frac{n}{2}\int (g(r)-1)V(r)dA\ ,$ where ...
0
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1answer
142 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?
2
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1answer
302 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 ...
8
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1answer
274 views

How does one get these definitions of the energy momentum tensor?

I was just reading a book - Mirror Symmetry by Clay Mathematics Institute, and on Page 402 of the book, the writer says that energy momentum tensor is defined classically by $$\delta S = -\frac{1}{4 ...
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0answers
117 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 ...
3
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1answer
263 views

Coulomb potential

It is known that the Coulomb potential can be obtained by Fourier transform of the propagator from E&M. Is this because one of Maxwell's equations have the form $\nabla \cdot \mathbf{E}=\rho$?
1
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1answer
405 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 ...
6
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1answer
306 views

Differential equation (Greens function) satisfied by the kernel using path integrals

I'm reading Feynman and Hibbs, Quantum Mechanics and Path Integrals. How do I show that the kernel $$\tag{2-25} K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$$ satisfies the ...
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2answers
151 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 ...
3
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0answers
90 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 ...
8
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1answer
179 views

Significance of Poles of Correlation Function in QFT

In QFT, specifically in scattering processes, what is the physical significance of the poles / residues of the $N$-point correlation function? And why?
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2answers
485 views

What does the sum of two qubits tell about their correlations?

How much can I learn about correlations between two quits by measuring the sum of their values? What is the best way to formalize such a question? Below is my original, longer formulation of ...
2
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1answer
127 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) ...