# Questions tagged [wick-theorem]

A combinatoric procedure in QFT of reducing arbitrary products of creation and annihilation operators to sums of products of pairs of these operators. A string of such operators is rewritten as the normal-ordered product of the string, plus the normal-ordered product after all single contractions among operator pairs, plus all double contractions, etc., plus all full contractions.

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### Non-perturbative matrix element calculation

Following Peskin & Schroeder's Sec.7's notation, I would like to compute the matrix element $$\left<\lambda_\vec{p}| \phi(x)^2 |\Omega\right>\tag{1}$$ where $\langle\lambda_{\vec{p}}|$ is ...
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### Doubt regarding use of Wick contractions

I'm currently taking my first course in QFT and am learning about finding transition amplitudes using Wick's theorem. As far as I'm aware, Wick's theorem gives us a way to change from a time-ordered ...
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### Greiner´s Field Quantization question [closed]

I upload a screenshot of Greiner´s book on QFT. I don´t understand one step. I need help understanding equation (3), what are the mathematical steps in between? Greiner, Field Quantization, page 245 (...
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### Relationship with double summing of $a_{\ell m}$

I would like to convince myself of the following relationship in an astrophysical context: \begin{aligned} & \sum_{m}\sum_{m^{\prime}}\left\langle a_{\ell m} a_{\ell m}^* a_{\ell m^{\prime}} a_{\...
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### Free fermion OPE

In Di Francesco's Conformal Field Theory, the propagator for the free Majorana fermion theory is given by $$\langle{\psi(z) \psi(w)}\rangle = \dfrac{1}{2\pi g} \dfrac{1}{z-w}$$ and the energy-...
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### Wick theorem for $N$-particle Matsubara green function: equal time contraction [duplicate]

I am wondering why, e.g., the book by Mahan, "Many-particle physics", mentions that contractions in Wick theorem for the $N$-particle Matsubara Green function between a pair of operators at ...
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### Wick's theorem and Feynman propagator

(this is the image from book 'No nonsense QFT' by Jakob Schwichtenberg, page no, 426) The quantity $[\phi_-(x),\phi_+(y)]$ is like an operator inside the bra-kets $\langle 0|$ and $|0\rangle$. I'm not ...
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### Two-point correlation function of two complex scalar fields

For a lagrangian: $$\mathcal{L}=\partial^\mu\phi_i^*\partial_\mu\phi_i-m_i^2|\phi_i|^2+\lambda(\phi_2^3\phi_1+\text{h.c.}).$$ where summation over $i=1,2$ is understood. I am trying to find the two ...
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### Spin and scale dimension of canonical spin-1/2 fields in (1+1)d

I am reading the book "Non-perturbative methods in 2 dimensional quantum field theory" by Abdalla, Abdalla and Rothe and have some questions about the Chapter 2.4 "Bosonization of ...
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### Multi-channel mean field theory

I have always been confused about the theoretical foundation of the mean field approximation. Below I follow the book Many-body Quantum Theory in Condensed Matter Physics by Bruus and Flensberg, ...
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### Wick contraction in quantum field theory

I am reading Anthony Zee's "Quantum Field Theory in a Nutshell" (1st edition). On page 47, when evaluating the 4-point Green's function $G_{ijkl}^{(4)}$ to order $\lambda$ using Wick ...
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### How one can use Wick's theorem for the product $A:\mathrel{B^{n}}:$?

I try to use Wick's theorem in the case that some products we deal with are already normal ordered. My guess is that it could be something like A:\mathrel{B^{n}}:~=~:\mathrel{AB^{n}}:+...
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### Does normal ordering (not) conflict with canonical commutators?

Normal ordering is pretty useful to stop expressions from diverging in quantum field theory and works out perfectly fine regarding this, but there is this little problem: Consider for example an ...
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### Wick's theorem on a four-point QED Green function in 2nd-order perturbation theory

Problem 13.1 in Mandl & Shaw's QFT. I need to calculate the second order contributions to the four point Green function $$\langle A^{\mu}(x_1)A^{\nu}(x_2)\psi(x_3)\bar{\psi}(x_4) \rangle,$$ ...
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### Calculating a four-point Green function using Wick's theorem (problem 12.1 in Mandl & Shaw)

In problem 12.1 in Quantum Field Theory, Mandl & Shaw the aim is to calculate the four point green function  G^{\mu\nu}(x,y,z,w) = \frac{\langle 0 | T\big(A^{\mu}A^{\nu}\psi(z)\bar{\psi}(w)S\big)...
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### Wick's Theorem Example from Stoof & Gubbels [duplicate]

I've been learning about Wick's theorem from a variety of sources when I came across this example from "Ultracold Quantum Fields" by Stoof et al. on page 148 (Here I have simplified the ...
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### Computing $\langle 0|S |0\rangle$ in $\phi^4$ theory [closed]

$\newcommand{\bra}[1]{\langle #1|}$ $\newcommand{\ket}[1]{|#1\rangle}$ I have been reading David Tong's QFT notes. As part of an exercise, I am asked to examine $\bra{0} S \ket{0}$ to order $\lambda^2$...
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### Normal ordered product of $4$ scalar fields $X^\mu$
I'm trying to get more familiarity with the conformal normal ordering used in Polchinski's String Theory vol. 1 and I'm currently trying to solve problem $2.2$ which asks to prove that the normal ...