# Tagged Questions

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, ...

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### Differentiating Propagator, Greens function, Correlation function, etc

For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most ...
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### Why correlation functions?

While this concept is widely used in physics, it is really puzzling (at least for beginners) that you just have to multiply two functions (or the function by itself) at different values of the ...
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### 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 states,...
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### 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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### Hamilton operator in absence of causal order?

I hope, this question isn't too broad or vague. In a recent paper, Ognyan Oreshkov et al. worked out a theory of quantum correlations in absence of any causal order, dropping the assumptions of a ...
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### What are Wightman fields/functions

Simple question: What are Wightman fields? What are Wightman functions? What are their uses? For example can I use them in operator product expansions? How about in scattering theory?
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### Contact Term and Schwinger Term

In field theory, when 4-divergences of time-ordered Green's functions are computed, there are extra terms known as 'Schwinger terms'. When deriving the quantum equations of motion for time-ordered ...
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### Mean of a measurement on periodic data: what is the use of the inverse of correlation length?

Correlation and autocorrelation is something that in my Bachelor's programme in physics has been somewhat overlooked, so I'm in trouble understanding their use in this paper (The prisoner’s dilemma on ...
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### How do I define time-ordering for Wightman functions?

This is a follow-up question to What are Wightman fields/functions Ok, so based on my reading, the field operators of a theory are understood to be operator-valued distributions, that is, to be ...
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### 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 (...
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### 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?
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### Can scattering amplitudes be simplified with 1PI diagrams?

I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
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### Symmetry factor for Feynman diagrams in $\phi^4$-theory for $n$-points Green function

I'm working with two theories. Theory A: $H_{int} =\int d^3x \frac{Mg}{2}\phi\varphi^2$ Theory B: $\phi^4$-interaction: $H_{int} = \int d^3 x \frac{\lambda}{4!}\phi(x)^4$ Where $M$ is the mass ...
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### How would Kohn-Sham orbitals differ from 'true' elecron wavefunctions?

How would the non-interacting electron orbitals from a perfect DFT solution for a given potential shape differ from the 'true' electron wavefunctions? Or can you only really talk about the total ...
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### Have the correlation functions of the XY spin chain model been calculated using a functional partition function with source terms?

Have the correlation functions of the XY spin chain model, $$H=-\sum_l (J_x \sigma_l^x \sigma_{l+1}^x+J_x \sigma_l^y \sigma_{l+1}^y)-B\sum_l \sigma_l^z$$ been calculated ...
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### Two-point function of a free massless scalar field in Euclidean space-time

Let $\phi(x)$ be a free massless scalar field on $d$-dimesnional space-time with Euclidean metric. I am interested in the operator formalism, i.e. $\phi(x)$ is an operator satisfying $\Delta \phi=0$ ...
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### 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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### 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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### 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 ...
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### Correlator of energy-momentum tensor and OPE

In http://arxiv.org/abs/hep-th/9108028 Equation (2.22), the correlation function of then energy-momentum tensor with some primary fields is We can view this as sum over the OPE of the energy-...
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### 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 ...
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### 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 ...
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 $\nabla \cdot \mathbf{E}=\rho$?