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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Feynman rule for scalar QED vertex
A popular problem in QFT textbooks and courses is to derive the Feynman rules for scalar QED. Usually, this theory is presented via the following Lagrangian density:
$$\mathcal{L} = (D_\mu\phi)^\...
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Number Operator "Ordering" for Higher Order Bosonic Operators
I'm considering the algebra of a single harmonic oscillator where $[\hat{a},\hat{a}^\dagger]=\hat{\mathbb{I}}$. Typically, one is interested in normal, antinormal or symmetric ordering. I am ...
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Correlation functions of exponentials of fields
I've been trying to solve for scattering amplitudes for 4 graviton scattering in string theory. However, while going through Schwarz, Witten and Green book for string theory, I come across the ...
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Equivalent definitions of Wick ordering
Let $\phi$ denote a field consisting of creation and annihilation operators. In physics, the Wick ordering of $\phi$, denoted $:\phi:$, is defined so that all creation are to the left of all ...
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Hartree-Fock Hamiltonian and higher-order terms
I'm diving into Hartree-Fock methods, and I'm confused on why the Hartree-Fock Hamiltonian reduces into a single particle Hamiltonian.
When applying Wick's theorem to the Fermi Sea vacuum, we use the ...
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Radial ordering in CFT
Consider the following quantum two-point function (without assuming radial time ordering),
$$\begin{align}
\langle 0 | \hat{T}(y)\hat{T}(z) |0 \rangle
& = \sum_{n,m}y^{-(m+2)}z^{-(n+2)}\...
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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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Wick's theorem for an interacting theory in the $n=4$ case
I was working with the following expression related to the Wick's theorem for four fermionic operators.
$$
\langle c^\dagger_i c_j c^\dagger_p c_q \rangle = \langle c^\dagger_i c_q \rangle \langle c_j ...
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How does one go about calculating non-time ordered correlation functions in scalar field theory?
I am aware that expressions for the time-ordered expectation values of field operators can be derived using Wick’s theorem. My question is, how would one go about finding the corresponding non-time-...
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Issue in Feynman propagator with derivative of a scalar field: which Feynman rule do I apply?
While solving a QFT exercise, I'm trying to calculate the Feynman propagator
$$
\underbrace{\partial_\mu \phi(x) \phi(y)} = \langle 0 \vert T { \partial_\mu \phi(x)\phi(y) } \vert 0\rangle
$$
where ...
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Confusion regarding simplifying normal ordered products in CFT
I am studying CFT on my own and have some confusion regarding applications of Wick's Theorem to simplify normal ordered products to time ordered products. Wick's theorem is fairly straightforward, ...
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Calculate first-order term of the $S$-matrix for the $\phi^{4}$ theory [closed]
Before I ask a question, I will start with a small introduction.
I want to evaluate the $S$-matrix order-by-order in an expansion in small $\lambda$ for a $2 \rightarrow 2$ scattering in $\phi^{4}$ ...
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Wick contraction between two scalar fields
I have a short question about Wick contraction.
It is given that $$\phi\left(x\right) = \phi^{+}\left(x\right) + \phi^{-}\left(x\right)\tag{1}$$ where:
$$\phi^{+}\left(x\right) = \int \frac{d^3p}{\...
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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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Doubt on scattering amplitude in scalar Yukawa theory
I'm currently following David Tong's notes on QFT. In the section on calculating transition amplitudes using Wick's theorem, he gives an example using a scalar Yukawa theory with real scalar field $\...
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