All Questions
Tagged with quantum-field-theory operators
715
questions
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107
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On which bundle do QFT fields live?
In QFT, there is a vector field of electromagnetism, usually notated by $A$, which transforms as a 1-form under coordinate changes. Since quantum fields are operator-valued, I thought it is a section ...
- 61
2
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2
answers
73
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How does inserting an operator in the path integral change the equation of motion?
I am reading this review paper "Introduction to Generalized Global Symmetries in QFT and Particle Physics". In equation (2.43)-(2.47), the paper tried to prove that when
$$U_g(\Sigma_2)=\exp\...
- 133
3
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1
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237
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Derivation of two-body Coulomb interaction in momentum space
$\newcommand{\vec}{\mathbf}$
In Condensed Matter Field Theory by Altland and Simons, they claim the two-body Coulomb interaction for the nearly-free electron model for a $d$-dimensional cube with side ...
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30
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Why the Slavnov operator is self-adjoint? [duplicate]
In the context of BRST we can define the Slavnov operator $\Delta_{BRST}$ which generates BRST transformations. My lecture notes claim that $\Delta_{BRST}$ is self-adjoint, but I don't see why.
- 305
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2
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114
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Do different bases of Fock space commute?
$\newcommand\dag\dagger$
Suppose we have a Fock space $\mathcal{F}$ with two different bases of creation and annihilation operators $\{a_\lambda, a^\dag_\lambda\}$ and $\{a_{\tilde \lambda}, a^\dag_{\...
3
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103
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The commutation relations of photon and gluon?
In QED, the photon field has the following commutation relations:
\begin{equation}
[A^{\mu}(t,\vec{x}),A^{\nu}(t,\vec{y})]=0, \tag{1}
\end{equation}
where $A^{\mu}(t,\vec{x})$ is the photon filed. ...
- 85
3
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1
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283
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Time-evolution operator in QFT
I am self studying QFT on the book "A modern introduction to quantum field theory" by Maggiore and I am reading the chapter about the Dyson series (chapter 5.3).
It states the following ...
- 521
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How to get $ H=\int\widetilde{dk} \ \omega a^\dagger(\mathbf{k})a(\mathbf{k})+(\mathcal{E}_0-\Omega_0)V $ in Srednicki 3.30 equation?
We have integration is
\begin{align*}
H =-\Omega_0V+\frac12\int\widetilde{dk} \ \omega\Big(a^\dagger(\mathbf{k})a(\mathbf{k})+a(\mathbf{k})a^\dagger(\mathbf{k})\Big)\tag{3.26}
\end{align*}
where
\...
- 31
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105
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Canonical commutation relation in QFT
The canonical commutation relation in QFT with say one (non-free) scalar real field $\phi$ is
$$[\phi(\vec x,t),\dot \phi(\vec y,t)]=i\hbar\delta^{(3)}(\vec x-\vec y).$$
Is this equation satisfied by ...
- 2,200
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Application of Callias operator in physics
In his article "Axial Anomalies and Index Theorems on Open Spaces" C.Callias shows how the index of the Callias-type operator on $R^{n}$ can be used to study properties of fermions in the ...
- 31
2
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1
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88
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Why does the mass term not violate particle number conservation in a free theory?
The Lagrangian of a free real scalar field theory is
$$ \mathcal{L} = \frac{1}{2} \partial_{\mu} \phi\; \partial^{\mu} \phi \; - \frac{1}{2} m^2 \phi^2. $$
If we decompose $\phi$ in terms of the ...
- 61
3
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1
answer
51
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Deriving OPE between vertex operator: Di Francesco Conformal Field Theory equation 6.65
How does one get Di Francesco Conformal Field Theory equation 6.65:
$$ V_\alpha(z,\bar{z})V_\beta(w,\bar{w}) \sim |z-w|^{\frac{2\alpha\beta}{4\pi g}} V_{\alpha+\beta}(w,\bar{w})+\ldots~?\tag{6.65}$$
...
- 327
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59
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Renormalization of the composite operator $\exp(\phi(x))$
I'd like to calculate $\langle\Omega|\exp(\phi(x))|\Omega\rangle$ for quartic scalar field theory (where $|\Omega\rangle$ is the interacting vacuum) and then renormalize to first order in the coupling ...
- 51
2
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2
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145
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Particle Creation by a Classical Source (on-shell mass momenta)
It is noted in Peskin and Schroeder's QFT text that the momenta used in the evaluation of the field operator $\phi(x)$ are "on mass-shell": $p^2=m^2$. Specifically, this is in relation to ...
- 4,399
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Why does a normal ordered product of operators (in CFT) have 0 expectation value?
Why does a normal ordered product of operators (in CFT) have 0 expectation value?
The definition (Francesco - Conformal field theory pg. 174) of the normal ordered product of two operators $A(z)$ $B(z)...
- 327