All Questions
Tagged with quantum-field-theory operators
715
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What is the meaning of twist in OPE?
In Operator Product Expansion (such as explained in Peaking) there appear a quantity for an operator called twist, defined to be $d-s$ where $d$ is the scaling dimension of the operator and $s$ is it'...
- 41
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1
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Quantization of a massless scalar
Let $t$:time, $r$:distance, and $u=t-r$.
Since any massless particle should propagate along u=const. , we need to change the asymptotic infinity of a massless scalar from time infinity to null ...
- 11
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1
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Non-Abelian anomaly: why does non-Hermitian operator have complete basis of eigenvectors?
In section 13.3 of his book [1], Nakahara computes the non-Abelian anomaly for a chiral Weyl fermion coupled to a gauge field by making use of an operator
$$
\mathrm{i}\hat{D} = \mathrm{i}\gamma^\mu (\...
- 2,157
3
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3
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Transition from position as operator in QM to a label in QFT
In David Tong's lecture "Quantum Field Theory" - Lecture 2, he said that
"In Quantum mechanics, position is the dynamical degree of the particle which get changed into an operator but ...
user385554
2
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1
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What's the exact definition of fields in conformal field theory?
For example we work with a 2d scalar field $\phi$. I guess $\phi$, $\partial_z\phi$, $\partial_{\bar z}\phi$ are fields, are there more? Is it true that all fields are in the form of $\partial_z^i\...
- 249
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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, ...
- 904
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State-Operator Correspondence and symmetry in CFT in general dimension
Let us assume to have a QFT ($\mathcal{L}$) with translational, Lorentz, scale and conformal invariance.
I ask because we can, for example the free scalar free theory, canonically quantize the system ...
- 194
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Action of Conjugate momentum $\hat{\pi}$ on $\hat{\phi}$ eigenstate [duplicate]
So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum Field Theory and the Standard Model"
and in the second requirement, he wanted me to show that the action of the conjugate ...
2
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2
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314
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CFT Radial Quantization Raising and Lowering Operators Sign Question [closed]
Following Slava Rychkov (Page 41, Or here on arxiv page 39), I am trying to show that the momentum operator raises the scaling dimension.
I've seen the other related questions on this matter by Y. ...
- 194
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Peskin & Schroeder equation (7.2)
I found this completeness relation of momentum eigenstate $|\lambda_p\rangle$
Here $|\Omega\rangle$ is the vacuum, and $|\lambda_p\rangle$ represents the state with one particle labeled by $\lambda$ ...
- 1
3
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Show that $i/2m\int d^3\vec x\hat\pi(\vec x)\partial^2_i\hat\phi(\vec x)=1/(2\pi)^3\int d^3\vec p E(\vec p)\hat a(\vec p)^\dagger\hat a(\vec p)$ [closed]
Show that the quantum field for the Hamiltonian, $$\hat H=\frac{i}{2m}\int d^3 \vec x\hat{\pi}(\vec x)\partial^2_i\hat{\phi}(\vec x)\tag{1}$$
can be written as $$\int \frac{d^3\vec p}{(2\pi)^3}E(\vec ...
- 295
2
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0
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77
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LSZ theorem for trivial scattering
The $1\to1$ scattering amplitude is trivial and is given by (take massless scalars for simplicity)
$$
\tag{1}
\langle O(\vec{p}) O^\dagger(\vec{p}\,')\rangle = (2 | \vec{p}\,|) (2\pi)^{D-1} \delta^{(...
- 181
1
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2
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188
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Squared spin operators in second quantization
Spin operator in second quantization can be written as:
\begin{equation}
\hat{\vec{S}}_{i} = \frac{1}{2} \sum_{\sigma \sigma'} \hat{c}^{\dagger}_{i\sigma} \hat{\vec{\sigma}}_{\sigma \sigma'} \hat{c}_{...
- 13
5
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2
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629
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Time ordering operator identity
In Ref. 1, the author states that:
Making use of the fact that in a chronological product factors with different time arguments on the path $C$ may be commuted freely, application of the group ...
- 8,094
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167
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Are creation and annihilation operators functions of momentum?
In QFT, we usually write creation and annihilation operators in the following way: ${a^s_{\textbf{p}}}^\dagger$, $a^r_{\textbf{q}}$, where $r,s$ denote the spins and $p,q$ the three-momenta of ...
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