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 to compute symmetry factors of Feynman diagrams: two-point correlation function of $\varphi^4$-theory up to the fourth order? [closed]
I'm a bit struggle with the computation of the symmetry factors of the 2-point correlation function in Feynman diagrams for the $\varphi^4$ theory. I'm using the formula found in "Gauge theory of ...
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Confusion regarding expression of Expectation Value in Quantum Mechanics
So, initially when I first learned Quantum Mechanics, the expectation value of the operator corresponding to a physical observable was given by : $$\langle \hat{Q} \rangle = \frac{\int_{-\infty}^{\...
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Relativistic Propagator for multi-particle states
In non-relativistic quantum mechanics, the transition amplitude for a system of $N$ particles is given by: \begin{equation} A = \langle\vec{q}_{1}|e^{-\frac{i}{\hbar}\hat{H}t}|\vec{q}_{2}\rangle \end{...
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Diagrammatic interpretation of the four-point correlation function in momentum space
In Peskin & Schroeder's book (chapter 7.2,p227), they claim that the exact 4-point function, expressed by $$ \left( \prod_{i=1}^{2} \int d^4 x_i \, e^{i p_i \cdot x_i} \right) \left( \prod_{i=1}^{...
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Why can we extract the value of $S$-matrix element by simply analyzing the pole of correlation function?
In Peskin & Schroeder's book (Chapter 7.2, p.223-226), they analyze the pole of the correlation function by discarding the exponential term. They first calculate the accurate value of the ...
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How to understand basics of propagators and Wightman function?
Professor David Tong, in QFT notes 2 at section 2.7 above eq. (2.90) writes: "Prepare a particle at spacetime point $y$. What is the amplitude to find it at point $x$? We can calculate this: $ \...
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Intuitive understanding for field strength renormalization
Suppose we are calculating some (general) 2-point function $\Sigma_n(p)$ at some order $n$ that contains at least one-loop. Let's say, for simplicity, $\Sigma_n$ diverges with one pole, so $$\Sigma_n(...
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Computing position two-point function and Fourier transform of $p^4 \ln p$
I am computing a two-point correlator in 4D Euclidean space and I am struggling with one particular term. I have found that in momentum space my correlator goes as $$\langle \mathcal{O}(p)\mathcal{O}(...
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6-point NMHV gluon amplitude using BCFW recursion diagrams
Doing some self-learning on the BCFW shift using spinor-helicity formalism, so essentially just wanted to know where I am going wrong when it comes to deciding which diagrams are valid or not. I am ...
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Dividing multi-particle states into a sum of states with particles of definite number
In Peskin & Schroeder's book (7.1 , p212) in the studying of the analytic structure of two-point correlation function, they generalize the completeness relationship of 1 particle states $$ \left( ...
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Why is this an out-of-time-order (OTOC) correlator?
I am trying to understand operator growth through the paper Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK by Qi and Streicher. It has equation 3.7, which is: $$ -\frac{1}{N}\sum_{j=1}...
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Why we exclude the Feynman propagators for external particles in Feynman rules of electrodynamics?
In Feynman rules of Quantum electrodynamics, to incoming/outgoing fermions/anti-fermions we do not attach the Feynman propagator $\frac{i(\not{p}+m)}{p^2-m^2+i\epsilon}$, but instead attach $u^r(\vec{...
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Is it true that every Feynman diagram can be divided into multiplication of one-particle irreducible diagrams? Is there a proof? [duplicate]
I've seen an explanation that every reducible diagram can be express as the multiplication of irreducible diagrams, however, if we simply multiply all irreducible diagrams together, wouldn't we be ...
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Tree-level of two-point function
I am currently learning AQFT (advanced QFT) with the lecture notes of Osborn (I've had a course on QFT but this was not with the path integral formalism) and at some point he says the following $$\...
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The electron vertex function: how is it possible? [closed]
I'm quite new to QFT and have some questions. 1 On the section 6.3 page 189 of Peskin & Schroeder QFT they evaluates diagram Which looks so strange because it seems like electron is interacting ...
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