# 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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### Expectation Value Of The Double Occupancy Operators' Product

I want to prove the relation \eqref{eq:Metz_relation} that i found in this article. \left\langle\varPhi_0\right|\prod_{i} \hat{D}_i\left|\varPhi_0\right\rangle= \left\langle\varPhi_0\...
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### Physical Meaning of the Gutzwiller Constraints

I have a doubt on the constraints for the expecation values obtained by Bünemann et all. First i want to introduce my notation To analytically solve a tight-binding model, \hat{H}= ...
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Let us define our path-ordered operator $\overrightarrow{U}\left(t_1,t_2\right)$: $$\overrightarrow{U}\left(t_1,t_2\right)=\overrightarrow{\mathcal{P}}\exp\int_{t_1}^{t_2}dt\,\mathcal{O}\left(t\... 2answers 155 views ### Radial ordered commutation relation In the book Conformal Field Theory of Francesco, Mathieu and Sénéchal, in Sec. 6.1.2, the authors state that the integral$$ \oint_w \mathrm{d}z~ a(z)b(w) ~=~ \oint_{C_1} \mathrm{d}z~ a(z)b(w) - \...
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In my String theory lecture radial ordering was introduced and I don't understand what it is. My first guess was $$R(A(z)B(w)) = A(z)B(w)\Theta(|z|-|w|) + B(w)A(z)\Theta(|w|-|z|).$$ But then we have ...
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### Symmetry factor in $\phi^4$ theory

I'm having trouble while trying to understand what the symmetry factor of a Feynman diagram really is. From books I get that it is a geometrical factor that you get by the number of ways in which you ...
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### Conformal transformation of a vertex operator before normal ordering

Let us consider a free scalar boson $\varphi(z,\bar{z})$ on the complex plane and assume the following two-point correlation function \begin{eqnarray} \langle\varphi(z,\bar{z})\varphi(w,\bar{w})\...
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### What exactly are we doing when we “invent” Feynman Diagrams?

So, I am trying to derive the Feynman rules for Yukawa theory (following the section in Peskin). Specifically, for the process 2 fermions $\rightarrow$ 2 fermions. To second order, I then have that ...
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### Problem with Wick's theorem (normal ordering of a contraction)

Taking the example of two bosonic fields, Wick's theorem is $$T\{\phi(x_1)\phi^\dagger(x_2)\} = N\{\phi\phi^\dagger\} + N\{(\phi\phi^\dagger)_c\}$$ where the subscript $c$ ...
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This is a follow-up question to QMechanic's great answer in this question. They give a formulation of Wick's theorem as a purely combinatoric statement relating two total orders $\mathcal T$ and $\... 1answer 4k views ### Why/How is this Wick's theorem? Let$\phi$be a scalar field and then I see the following expression (1) for the square of the normal ordered version of$\phi^2(x). \begin{align} T(:\phi^2(x)::\phi^2(0):) &= 2 \langle 0|T(\... 1answer 76 views ### What is the calculation rule of the normal ordering operator? Here\phi_I$is just the free Klein-Gordon field. So, this field is decomposed of two components shown above. Now let$N$be the normal ordering operator. Then, I think that$N(\phi_I^+(x)\phi_I^-(y))...
Consider Exercise 2.8 in Polchinski's String Theory book. We are asked to compute the weight of $$f_{\mu \nu}:\partial X^{\mu} \bar{\partial}X^{\nu}e^{ik\cdot X}:$$ I have carried out the usual ...