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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
4 views

Photon number autocorrelation in Cavity QED

I am studying this paper dealing with optomechanical strong coupling, and I don't understand one very relevant part of it. In particular, the authors define (equation (8)) a photon number ...
user avatar
1 vote
1 answer
44 views

Peskin & Schroeder QFT,eq. (2.56) derivation

I'm trying to derive the eq.2.56 of P&S's QFT textbook step by step: $$(\partial^2+m^2)D_R(x-y)=-i\delta^{(4)}(x-y). \tag{2.56}$$ I have no problem with the first step: $(\partial^2+m^2)D_R(x-y)=(\...
user avatar
1 vote
1 answer
40 views

The relation between full Green's function and S-matrix

I'm learning Green's function in condensed matter. The full Green's function is defined as $$G(k_2,t_2;k_1,t_1) = <\Omega |T a_{k_1}(t_1)a_{k_2}^{\dagger}(t_2) |\Omega> $$ The $\Omega$ is the ...
user avatar
0 votes
0 answers
24 views

Understanding inelastic neutron scattering intensities

Inelastic neutron scattering (INS) is commonly used to probe the magnetic structure of materials and to probe magnetic excitations (magnons) in a system. Unpolarized INS measures the spin-spin ...
user avatar
0 votes
1 answer
34 views

Explicit check of Ward identity (Peskin & Schroeder p. 160)

I am trying to check explicitly that the (Compton) amplitude $$i\mathcal{M} = -ie^2\epsilon^*_\mu(k’)\epsilon_\nu(k)\bar u(p’)\left[\frac{\gamma^\mu \not k\gamma^\nu + 2\gamma^\mu p^\nu}{2p\cdot k}+\...
user avatar
  • 441
0 votes
0 answers
24 views

Propagators in Quantum Field Theory at Finite Temperature

While reading section 5.8.2 of Quantum Field Theory An Integrated Approach by Fradkin, I had a few questions, not able to think them though myself. The thermal propagator is given as $$G_{T}^{(0)}(\...
user avatar
  • 61
2 votes
1 answer
51 views

Wick's Theorem and Functional Derivative

In the Quantum Field Theory An Integrated Approach, Fradkin, the author derived the partition functional for a free scalar field (after analytic continuation to imaginary time ) as $$Z_{E}[J]=Z_{E}[0] ...
user avatar
  • 61
2 votes
0 answers
56 views

Struggling with Peskin and Schroeder equation (12.49) and the constraint of renormalizability

In peskin and schroeder it's written that any renormalizable massless scalar field theory has a 2-point greens function of the form: I don't get how we can know that the 1-loop diagrams have exactly ...
user avatar
2 votes
1 answer
44 views

Onsager's hypothesis: why is true that correlations decay with increasing time?

I am studying from Chandler's book (Introduction to Modern Statistical Mechanics) the fluctuation-dissipation theorem. Before introducing it, the book states something without really demonstrating it. ...
user avatar
1 vote
0 answers
30 views

Correlation function of 4-currents on a general QFT

Given $V^\mu(x)$ a 4-current of a general unitary, Poincaré invariant QFT, I need to show that the correlation function: $$iC_{\mu\nu}(x-y) = \langle {\tilde{0}}|T\left[V_\mu(x)V_{\nu}^\dagger(y)\...
user avatar
  • 21
0 votes
0 answers
49 views

Why does this particular Diagram in Third Order $\Phi^4$ theory not contribute?

In this question Moeman asked a question about third order Feynman diagrams in $\phi^4$ theory. I am also working on this problem now on my own and encountered the diagram illustrated below, which ...
user avatar
  • 1,226
0 votes
0 answers
20 views

The confusion over the invariance of the correlation function and the mutually local field in the CFT

Consider the correlation function $$\langle \Pi_{i=1}^n V_i(z_i,\bar z_i) \rangle$$ such as $$\langle V_1(z_1) V_2(z_2) \rangle,(z_1>z_2)$$ by position the $z_i$ correctly, the exchange of the ...
user avatar
0 votes
0 answers
32 views

Computing the anomalous dimension of $\phi^2$ via Peskin and Schroeder

I am trying to understand the example that Peskin and Schroeder present at section 12.4 where they calculate the AD of $\phi^2$. Specifically they give a renormalization condition in 12.113 which does ...
user avatar
1 vote
1 answer
38 views

Momentum conservation in correlation functions

In Mahan "Many particle physics" the following Hamiltonian is considered in studying electron tunnelling through a junction \begin{equation} H_t = \sum_{kp} T_{kp} c^\dagger_k c_p + h.c. \...
user avatar
2 votes
0 answers
73 views

Why does the LSZ reduction formula only give the connected part of the $S$ matrix?

As an example, using the LSZ reduction formula, the $S$ matrix element for $2\rightarrow 2$ scattering is found in Peskin and Schroeder to be $$\langle \boldsymbol{p}_1 \boldsymbol{p}_2\rvert S \lvert ...
user avatar
  • 1,297
1 vote
1 answer
48 views

Why is pair distribution function equal to the Boltzmann factor?

On my statistical physics book it is written that the probability of finding two molecules at distance $r$ is not influenced by the presence of the other molecules, and for this reason, without any ...
user avatar
  • 1,398
5 votes
1 answer
117 views

Peskin and Schroeder Exercise 10.2 - Yukawa Theory Renormalization

I am having some trouble with exercise 10.2 in Peskin and Schroeder, on the renormalization of Yukawa theory. Part a) of the exercise says show that the theory contains a superficially divergent 4$\...
user avatar
  • 63
1 vote
0 answers
33 views

Schwartz's derivation of the Feynman rules for scalar fields

In his book "Quantum field theory and the standard model", Schwartz derives the position-space Feynman rules starting from the Schwinger-Dyson formula (section 7.1.1). I have two questions ...
user avatar
  • 71
0 votes
0 answers
31 views

Large Scale Structure: Math proof that power spectrum being zero at a scale means fluctuations have variance of underlying Gaussian field

(Please don't close this one as a homework question. I am self taught and I have no way to get this information from any other source besides asking it here.) I am trying to solve this question (11.6) ...
user avatar
  • 1
0 votes
0 answers
17 views

EMT in 2D Euclidean Yang Mills

In pure 2D Euclidean YM theory with $SO(8)$ gauge group. For Lagrangian $\frac{1}{4g^2} Tr(F_{\mu\nu}F^{\mu\nu})$ is energy momentum tensor $$T^{\mu\nu}=\frac{1}{g} Tr(-F^{\mu\rho}F_\rho^\nu+1/4\eta^{...
user avatar
  • 145
0 votes
0 answers
43 views

Physical interpretation of FFT frequencies

I need to calculate the PSD of a discrete signal and want to compare it to other processes. By Nyquist theorem, I only can account half of the frequencies. Assume I have a signal of length $N=100$, ...
user avatar
0 votes
0 answers
37 views

What is the meaning of a propagator of a Dirac field and how to get a probability of a process from it?

Let me first present what is my understanding of a propagator. What we measure in the experiment is a probability of scattering. We try to construct a theory predicting these measurements. What we are ...
user avatar
1 vote
1 answer
70 views

LSZ formula for initial and final one particle states

The LSZ formula for a real scalar field $\varphi$ is (Srednicki 5.24) $$ \left<f|i\right>=i^{n+n'}\int d^4x_1e^{ik_1x_1}(-\partial_1^2+m^2)...\\ \quad d^4x'_1e^{ik'_1x'_1}(-\partial_{1'}^2+m^2).....
user avatar
  • 83
0 votes
1 answer
67 views

Calculating some functional derivative

I am reading Mark Srednicki's quantum field theory, p.50~p.52 (Part I section 7). In the section, he derives a the formula for the ground state to ground state transition amplitude of harmonic ...
user avatar
0 votes
1 answer
55 views

Compute the generating functional for the $bc$ theory

I need the generating functional for the $bc$ CFT, which has $$L=\frac{1}{2\pi}(b\bar{\partial}c + b\partial\bar{c}),$$ so I can compute the correlation function $$\langle b(z_1)c(z_2)\rangle =\frac{1}...
user avatar
0 votes
0 answers
43 views

Intuitive Approach to Wick's Theorem

Context I'm currently reading Many-Particle Physics by Gerald D. Mahan. In section 2.4 it explains Wick's theorem and he gives the example $$ _0\langle|T \hat{C}_\alpha(t) \hat{C}_\beta^\dagger(t_1) \...
user avatar
  • 776
2 votes
1 answer
72 views

Conformal symmetry and cluster decomposition?

I would expect a conformal field theory would not satisfy a cluster decomposition of correlation functions. This may be due to my lack of understanding of conformal symmetry, but I would think a ...
user avatar
  • 3,294
0 votes
1 answer
32 views

What does a local maximum under 1 in a two-point correlation function mean?

Two-point correlation functions like the radial distribution function (real space) and the structure factor $S(q)$ (reciprocal space) give information about correlations in a (typically) fluid ...
user avatar
1 vote
0 answers
22 views

How to apply the boundary condition in the derivation of the 2-point function in MAGOO?

In the famous AdS/CFT review, in section 3.3.1 the authors give the two-point function of the operator $\mathcal{O}$ for which $\phi_0$ is a source, we write $$ \langle\mathcal{O}(p)\mathcal{O}(q)\...
user avatar
1 vote
0 answers
44 views

Why is the Propagator given by the Green's Function for a General Field in Canonical Quantisation?

In canonical quantisation, it is taught that the propagator for the Klein-Gordon field is defined as $$\Delta_F(\vec x - \vec y) \equiv \left < 0 \right | \overleftarrow{\mathcal T} \phi(\vec x) \...
user avatar
0 votes
0 answers
41 views

Uniform radial distribution function

I am attempting to properly account for excluded volume effects on the radial distribution function for a fluid. A correction for these effects has been proposed back in 2000 in this paper by Hartnig ...
user avatar
  • 1
1 vote
0 answers
52 views

MAGOO 2-Point Correlation function derivation

I am studying the famous MAGOO review and I am trying to understand section 3.3 where we calculate the correlation functions from the AdS side. In subsection 3.3.1 the authors go through the 2-point ...
user avatar
0 votes
1 answer
56 views

Correlation Function and Generating Functional in QED

Peskin and Schroeder (1995, p.82 and p.292) define the two-point correlation function of a $\phi^4$ theory as $$\langle \Omega|T\{\phi(x)\phi(y)\}|\Omega\rangle\tag{4.10}$$ and the generating ...
user avatar
  • 375
1 vote
0 answers
32 views

Observables from boson correlation functions

I am studying the formalism of quantum optics in the approximation of a two-level system coupled to a reservoir made of boson in thermal equilibrium. As usual, the latter subsystem is described in ...
user avatar
1 vote
0 answers
13 views

Quantum analog of mixing time correlation functions

Classical ergodic theory predicts that in maximally chaotic systems correlation functions relax to the long time limit \begin{equation} \langle A(0) B(t)\rangle_0 \to_{t\to+\infty} \langle A\rangle_0 \...
user avatar
  • 365
1 vote
1 answer
67 views

Shift in renormalized Green's function

In chapter 12.2 p. 410 of Peskin and Schroeder the Callan-Symanzik equation is derived. I understand the relation between (connected) renormalized and non-renormalized Green's functions given by $$ G^{...
user avatar
1 vote
1 answer
77 views

Is the retarded propagator exactly the Green's function?

I am trying to prove that, for the real scalar field $\phi(x)$, the retarded propagator, which is defined as $$ D_{R}(x-y)=\theta(x^0-y^0)\langle 0 |[\phi(x),\phi(y)]|0\rangle $$ is the Green's ...
user avatar
  • 125
8 votes
1 answer
111 views

Why the Feynman diagrams contributing to the effective action $\Gamma[\phi_{\rm cl}]$ are stripped/amputated/have no external lines?

I am reading P&S Chapter 11 and specifically I am trying to understand the derivation of $\Gamma[\phi_{\rm cl}]$. All the algebra is okay, but I am failing to understand the connection to Feynman ...
user avatar
  • 467
3 votes
0 answers
55 views

Confusion on two-point correlation function in momentum space

I am trying to understand the two-point correlation function of a massless complex scalar field in momentum space. My attempt is given below: Let $\phi$ is a complex scalar field and $\bar{\phi}$ is ...
user avatar
  • 31
2 votes
0 answers
78 views

On-shell propagator to an off-shell propagator

I am learning the Ward-Takahashi Identity part of Peskin and Schroeder's textbook of quantum field theory. In the prove process, it involves a diagram 7.66. Then it says that I can understand ...
user avatar
  • 75
0 votes
0 answers
73 views

Two-point correlation function with interactions

I am reading Peskin & Schroeder page 289. They discuss only very briefly the path integral for the $\phi^4$ theory. Therefore I am unsure if I understand the main point. They consider $$\mathcal{L}...
user avatar
2 votes
1 answer
97 views

Two-point correlation function for scalar fields derivation

I am reading Peskin and Schroeder section 9.2. I don't understand the step when they evaluate equation (9.18) $$<\Omega| T \phi_H(x_1)\phi_H(x_2)|\Omega>= {\rm lim}_{T\to \infty (1-i\epsilon)}\...
user avatar
4 votes
3 answers
82 views

PCAC - Ward Identity for non-conserved currents - Derivative and $T$-Order Commutation

I'm currently studying Goldberger-Treiman relation from the book by S. Coleman (Aspects of Symmetry, chapter 2) in which, working in the framework of a not better precised "weak interaction ...
user avatar
0 votes
0 answers
37 views

Power-Spectrum for Self-Organised Criticality

In 1987 Bak, Tang and Weisenfeld authored a paper (link) on Self-Organised Criticality, on how minimally stable self-organised systems propagate the perturbations it is subjected to, scale-freely - ...
user avatar
1 vote
0 answers
46 views

Scalar Yukawa theory, contraction

In the scalar Yukawa theory ($\Phi$ is real scalar field and $\phi$ is a complex scalar field): \begin{equation} \mathcal{L}_{S Y}=\left(|\partial \phi|^{2}-m^{2}|\phi|^{2}\right)+\frac{1}{2}\left((\...
user avatar
5 votes
1 answer
230 views

Propagator of four-dimensional Chern-Simons theory

In https://arxiv.org/abs/1903.03601, on page 13, the propagator of 4d Chern-Simons theory is computed, in the gauge $D^iA_i=0$, where $D^i = (\partial_x,\partial_y,4\partial_z)$. The gauge-fixed ...
user avatar
  • 1,129
0 votes
1 answer
61 views

Real-space correlations of massless Majorana fermions

Consider an action of free, massless Majorana fermions in real time and 1+1 dimensions of the form $$ S[\psi] = \frac{1}{2} \int d^2x \ \psi^{T}\gamma^0 (i \gamma^{\mu} \partial_{\mu}) \psi $$ Here, $\...
user avatar
  • 1,814
2 votes
0 answers
170 views

Can the $S$-matrix always be decomposed as $S = 1 + iT$?

The LSZ formula for a scalar field $\phi$ with $n$ out-states and $r$ in-states is $$ \langle p_1,\dots,p_n\vert S \vert q_1,\dots, q_r \rangle = \left(\mathrm{i}Z^{-1/2}\right)^{n+r}\prod_i (-p_i^2 + ...
user avatar
  • 2,282
0 votes
1 answer
65 views

LSZ formula applied to two-point correlation function

I was trying to find the scattering amplitude using the LSZ formula for a trivial process i.e. applying it to the two-point correlation function, but I kept getting 0 as the answer. I'm not sure ...
user avatar
  • 2,282
1 vote
0 answers
32 views

What is the meaning of region momentum (or dual momenta) variables in the worldsheet?

In scattering amplitudes, we deal with usual momentum variables which flow across any edge in a Feynman diagram. For a colour ordered amplitude, we can further designate region momenta to the planes ...
user avatar

1
2 3 4 5
13