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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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How does inserting an operator in the path integral change the equation of motion?

I am reading this review paper "Introduction to Generalized Global Symmetries in QFT and Particle Physics". In equation (2.43)-(2.47), the paper tried to prove that when $$U_g(\Sigma_2)=\exp\...
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Could the gamma ray burst on 12/27/2004 caused the Tsunami on 12/26/2004? Is there a pressure wave in front of the blast? [closed]

Tsunami on 12/26/2004 Gamma ray blast on 12/27/2004 that ionized the stratosphere
sean duren's user avatar
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Are strong correlations of boundary spins possible in the absence of long-range order in the bulk?

Question about one-dimensional models with short range interaction of quantum spins, such as transverse Ising and Heisenberg models. Are there any examples when, in the ground state of the system, the ...
Gec's user avatar
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Correlation function of a two-level quantum system coupled to a thermal bath

I am trying to quantify the temporal correlations of observables in an open quantum system, i.e. calculate a quantity of the type, \begin{equation} \langle n(t) n(t') \rangle - \langle n(t)\rangle \...
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Laplace Transform of time evolution of Amplitudes involving correlation functions

The correlation function is given by $$ G_{ij}(t-t')= g_{i} g_{j} e^{(i\omega_{i0}-\frac{\Gamma_{0}}{2})t-(i\omega_{j0}-\frac{\Gamma_{0}}{2})t'} $$ With the time evolution of amplitudes being given by ...
Ashish Anil's user avatar
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Goldstone Theorem in Schwartz, follow-up

This is somewhat of a related question to Goldstone theorem in Schwartz and is related to equation 28.16 in Schwartz's QFT book. One way to prove that $$ \langle \Omega | J^\mu(x) | \pi(p) \rangle = i ...
infinity's user avatar
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What is the relationship between persistence length and timescale?

I have calculated the bending persistence length of a polymer using MD simulations in the nanosecond timescale. The persistence length is long (410 nm) compared to the contour length (40-45 nm). But ...
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Conceptual Difference Between OPE and Propagator

I'm specifically working with a 2d free scalar CFT. In this case, the propagator is $$\langle X(\sigma) X(\sigma')\rangle=-\frac{\alpha'}{2}\ln(\sigma-\sigma')^2\tag{p.78}$$ while the OPE between $X(\...
Sam's user avatar
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Why does an all connected diagram contribute to two-point function?

I am recently reading E.Witten's review for $1/N$ expansion of QCD. In there, considering the main contribution of quark bilinears like $\bar{q}q$, then He mentions that in free field theory there is ...
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Keldysh rotation and Langreth theorem

Given a (Green) function of two time arguments on the Keldysh contour $g(\tau_1, \tau_2)$, we can distinguish between four cases, depending on whether each contour time lies on the forward or reverse ...
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Calculating higher-order correlation functions of the Ising model

I'm trying to compute the correlation functions $<s_1...s_n>$ of specific n-spin subsets as a function of the temperature in systems with up to $N=256^2$ spins. These will be used to compute ...
Ibrahim Khalil's user avatar
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Bulk-to-bulk propagator in 3-point function in AdS-CFT correspondence. Trouble solving a PDE

I have encountered an issue in a PDE (A Green's function actually). I am solving it in $(d+1)$-dimensions and I use Poincare coordinates in AdS spacetime, meaning I have a dimension $z$ and I also ...
Βασίλης Γερμανίδης's user avatar
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Trouble in complex integral while calculating 2-point function in AdS-CFT correspondence [closed]

Upon calculating the 2-point function of a scalar, I ran in a problem in the final calculations. For reference, I am basiccaly following the methodology of https://www.sissa.it/tpp/phdsection/...
Βασίλης Γερμανίδης's user avatar
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QED: Structure of electron vertex function in the massless limit

I am working my way through Peskin & Schröder's "Introduction to QFT". In section 6.2, the formal structure of the electron vertex function $\Gamma^\mu$ is considered. From Lorentz ...
James Bates's user avatar
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Quantum fields can leak out of the light cone? [duplicate]

So the transition amplitude for a free Klein-Gordon field for a space-like interval is finite and non-vanishing (decays exponentially). What does one make of this physically, i.e. what is the meaning ...
Albertus Magnus's user avatar
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Do coupling constants change under length rescaling?

I am studying renormalization in the Skinner's notes https://www.damtp.cam.ac.uk/user/dbs26/AQFT/Wilsonchap.pdf and I can't understand the passage in formula (5.22) $$\Gamma^{(n)}_{\Lambda}(x_{1},...,...
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Green Kubo Relation for viscosity

I am calculating viscosity of WCA fluid using the Green Kubo relation. I am also following the paper of Zhang et al. for the Time decomposition method https://doi.org/10.1021/acs.jctc.5b00351 where, ...
Lifelong Learner's user avatar
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Correlation functions of exponentials of fields

I've been trying to solve for scattering amplitudes for 4 graviton scattering in string theory. However, while going through Schwarz, Witten and Green book for string theory, I come across the ...
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References on getting the correlation function in a 3D Markov Random Field?

Does anyone know where to look to find analytical formulae for the correlation function of the Ising model on a 2D or 3D lattice (assuming toroidal or infinite is easier?), or, even better, a ...
seeker_after_truth's user avatar
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1 answer
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What's the minima of the quantum effective action?

Consider the vacuum expectation value of a (for simplicity scalar) field $\phi$, we know that its vacuum expectation value can be expressed as $$\langle\phi\rangle=\frac{1}{\mathcal{Z}}∫\mathcal{D}\...
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A question on IR divergence in Peskin-Schroeder chapter 6

In equation 6.64 of Peskin Schroeder, it computes $f_{\text{IR}}(q^2)$ in the limit $-q^2\to\infty$. Now, if we try to simplify the integral: \begin{align} f_{\text{IR}}(q^2) &=\int_0^1d\xi\;\frac{...
Soumyajit Datta's user avatar
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What is the signal of a spin wave?

From what I understand, for example in the Ising model, we can probe the correlation function via neutron scattering, and the correlation function gives the magnetic susceptibility for the system. Is ...
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Why are 2-point functions Green's functions?

I asked a question about this earlier but I think it was unfocused so I have rephrased it and asked it again. The propagator/two-point function $\langle \phi(x_1)\phi(x_2)\rangle$ for any theory can ...
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Is there any intuitive reason why 2-point functions are inverse operators to the free Lagrangian? [duplicate]

To compute $n$-point functions in quantum field theory we use Wick's theorem to reduce this problem to computing 2-point functions. In many textbooks, such as Peskin & Schroeder, the 2-point ...
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Why do correlation functions involving composite fields require special analysis?

For simplicity I will be considering $\phi^4$ theory. To analyze correlation functions of the form $$\langle \phi(x_1)\phi(x_2)\ldots\phi(x_n)$$ with $$x_1 \neq x_2 \neq \cdots \neq x_n \tag{1}$$ we ...
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Understanding $W^{(n)}$, $\Gamma^{(n)}$, and $\Sigma$ in Feynman diagrams

In quantum field theory (specifically $\phi^4$ theory), $W$ is the sum of all connected Feynman diagrams and the effective action $\Gamma$ is the sum of all 1PI Feynman diagrams. They are related by a ...
CBBAM's user avatar
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Does path intergral formula only works in perturbative situation?

I'm learning quantum field theory. In Peskin & Schroeder, when they derive $$\int {D\phi(x)\phi ({x_1})\phi ({x_2})\exp [i\int {{d^4}x\mathcal{L(x)}] = \left\langle {{\phi _b}|{e^{ - iHT}}T\{ \phi ...
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Correlation length in a 3d Ising slab with one dimension much smaller than the other two

Suppose I have a 3d Ising model on a cubic lattice, but one of its dimensions is much smaller than the other two. That is, I have an $L$ by $L$ by $L'$ slab with $L' << L$; in particular, $L'$ ...
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1 vote
1 answer
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How are general quantum correlation functions actually measured?

These days, the majority of work in theoretical particle, condensed matter, and AMO physics is about methods for calculating exotic correlation functions, of the rough form $$G_{ij} \sim \langle \...
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A question on emission spectrum and two-time correlation function

Here, the expression of the emission spectrum is $$S(\omega)=\int_{-\infty}^{\infty}\langle A^\dagger(t+\tau)A(t) \rangle e^{-i\omega\tau}\text{d}\tau=2\Re\left\{\int_{0}^{\infty}\langle A^\dagger(t+\...
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2 votes
2 answers
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Why $n-1$ point function vanishes in $D=0$ scalar theory?

If we consider a $D=0$ theory with the Lagrangian: $$\mathcal{L}[\phi]=g\phi^n+J\phi$$ And its Green functions: $$G_n=\langle\phi^n\rangle_{J=0}=\frac{1}{Z[0]}\frac{\delta^nZ[J]}{\delta J^n}|_{J\...
Errorbar's user avatar
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1 vote
1 answer
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Time ordered correlator from path integral: equation of motion?

Consider a Lagrangian $L(\phi)$ for a field $\phi$ (assume it is a free real scalar for simplicity). Then the time ordered propagator can be expressed as a path integral $$ \langle\Omega|T\{ \phi(x) \...
QuantumEyedea's user avatar
1 vote
0 answers
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Furry's theorem in Electroweak and strong interactions

We can think of Furry's theorem as the consequence of $CP$ invariance of $QED$. For parity, the vector bilinear changes sign, hence, under charge conjugation, it should. The vacuum is $C$-invariant, ...
Tanmoy Pati's user avatar
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1 answer
113 views

Why is a fluctuating light source is required for classical ghost imaging?

This paper mentions two conditions crucial for the classical ghost imaging experiment which are:- the spatial incoherence of light, and a measurement time $\ll \tau_{coh}$. Why is the spatial ...
QuantumOscillator's user avatar
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1 answer
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Correlation time of speckle pattern

I am setting up classical ghost imaging. I am trying to reproduce the results by this paper. It mentions that crucial things to get the experiment to work is spatial incoherence and measurement time ...
QuantumOscillator's user avatar
1 vote
1 answer
48 views

Translational Correlation function

I have to compute the translational correlation function of a 2 dimensional set of particles. The function is given in literature like following: $$ G_k(r) = \sum_{l = 1}^6\frac{1}{N}\sum_{<j,k>}...
David Lamprecht's user avatar
3 votes
1 answer
93 views

Amputated connected 2-point function is inverse to connected 2-point function

Let $D_n$ denote the $n$-point correlation function consisting of only connected diagrams. We may decompose this as an integral of two products. The first factor consists of a product over the $n$ ...
CBBAM's user avatar
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2 votes
0 answers
37 views

Double Discontinuity In CFT

In the paper Analyticity in Spin in Conformal Theories Simon defines the double discontinuity as the commutator squared in (2.15): $$\text{dDisc}\mathcal{G}\left(\rho,\overline{\rho}\right)=\left\...
ssm's user avatar
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Radial ordering in CFT

Consider the following quantum two-point function (without assuming radial time ordering), $$\begin{align} \langle 0 | \hat{T}(y)\hat{T}(z) |0 \rangle & = \sum_{n,m}y^{-(m+2)}z^{-(n+2)}\...
phonon's user avatar
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Next-to-leading $1/N$ contributions to Feynman diagrams in large $N$

I want to understand $1/N$ contributions to quark bilinear operators $J(x)$ in large $N$, for instance, operators of the form $q\bar{q}$ or $\bar{q}\gamma^\mu q$. As pointed out by E. Witten, in the ...
Spectree's user avatar
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Quantum Regression Theorem Assumptions

The Quantum Regression Theorem states that if the time evolution of single-operator expectation values is known, then this determines the time evolution of higher-order correlations.Mathematically we ...
Testina's user avatar
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Correspondence between Feynman diagrams in the $n$-point correlation function expansions for 2 different cutoffs

My understanding of QFT is quite elementary. I'm reading through Kevin Costello's book on Renormalization and effective field theory, which is based on Wilsonian low energy theory. The integral for an ...
Yashasvi Aulak's user avatar
5 votes
1 answer
233 views

How does one rigorously define two-point functions?

Let $\mathscr{H}$ be a complex Hilbert space, and $\mathcal{F}^{\pm}(\mathscr{H})$ be its associated bosonic (+) and fermionic (-) Fock spaces. Given $f \in \mathscr{H}$, we can define rigorously the ...
MathMath's user avatar
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1 vote
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Planar spin in two-dimensional CFT

I have several questions regarding the definition of planar spin. I was reading the big yellow book (by Di Francesco et. al.) Section 5.1.5 looks a little mysterious. Look at 5.25, which is the two-...
hossein mohammadi's user avatar
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1 answer
71 views

Relation between Mean Squared Displacement and Velocity Autocorrelation Function [closed]

I'm trying to understand the relation between the Mean Squared Displacement in a sample of moving atoms (for example) and the autocorrelation function of the velocity. So I read in "Understanding ...
chewingram's user avatar
1 vote
1 answer
125 views

Wick's theorem for an interacting theory in the $n=4$ case

I was working with the following expression related to the Wick's theorem for four fermionic operators. $$ \langle c^\dagger_i c_j c^\dagger_p c_q \rangle = \langle c^\dagger_i c_q \rangle \langle c_j ...
Bio's user avatar
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Zero temperature Green function as limit of finite temperature Green function

Consider a system of $N$ fermions in a periodic box $\Lambda \subset \mathbb{R}^{d}$. The Hamiltonian of the system is: $$H_{N} = \sum_{k=1}^{N}(-\Delta_{x_{k}}-\mu) + \lambda \sum_{i< j}V(x_{i}-x_{...
MathMath's user avatar
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2 votes
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Do we have "amplitudes over configurations over spacetime" for QFT in terms of path integral?

Suppose we work in 1+1 spacetime and consider only a scalar field. In canonical quantization of QFT, a state is a density on "configuration on a time slice" (Let's forget the fact that there ...
Peter Wu's user avatar
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0 answers
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How does one go about calculating non-time ordered correlation functions in scalar field theory?

I am aware that expressions for the time-ordered expectation values of field operators can be derived using Wick’s theorem. My question is, how would one go about finding the corresponding non-time-...
Jack's user avatar
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2 votes
2 answers
173 views

Existence of low temperature phase in 2-Dimensional XY-Model

I'm reading the lecture notes of David Tong on Statistical Field Theory, specifically chapter $4.4$ on the Kosterlitz-Thouless Transition. He considers the XY model in $d=2$ dimensions and states the ...
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