All Questions
Tagged with quantum-field-theory operators
715
questions
1
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2
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201
views
Using Wick's Theorem in an example with the harmonic oscillator
I understand Wick's theorem to be,
$$T(x)=\mathcal{N}(x)=\sum:\textbf{all contractions}:$$
And I'm researching combinatorics and quantum theory in general.
How would one connect Wicks theorem to the ...
CommunityBot
- 1
2
votes
2
answers
81
views
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
$$U_g(\Sigma_2)=\exp\...
- 589
1
vote
0
answers
122
views
On which bundle do QFT fields live?
In QFT, there is a vector field of electromagnetism, usually notated by $A$, which transforms as a 1-form under coordinate changes. Since quantum fields are operator-valued, I thought it is a section ...
- 936
3
votes
1
answer
249
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Derivation of two-body Coulomb interaction in momentum space
$\newcommand{\vec}{\mathbf}$
In Condensed Matter Field Theory by Altland and Simons, they claim the two-body Coulomb interaction for the nearly-free electron model for a $d$-dimensional cube with side ...
- 8,094
0
votes
0
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31
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Why the Slavnov operator is self-adjoint? [duplicate]
In the context of BRST we can define the Slavnov operator $\Delta_{BRST}$ which generates BRST transformations. My lecture notes claim that $\Delta_{BRST}$ is self-adjoint, but I don't see why.
- 207k
0
votes
2
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116
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Do different bases of Fock space commute?
$\newcommand\dag\dagger$
Suppose we have a Fock space $\mathcal{F}$ with two different bases of creation and annihilation operators $\{a_\lambda, a^\dag_\lambda\}$ and $\{a_{\tilde \lambda}, a^\dag_{\...
- 5,989
2
votes
1
answer
468
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Primary fields in di Francesco's CFT
In the CFT book by Di Francesco et al. they use conventions such that part of the conformal algebra (see eq. 4.19) is
$$
[D,P_\mu]=iP_\mu, \\
[D,K_\mu]=-iK_\mu, \tag{1}
$$
where $P_\mu$, $D$ and $K_\...
CommunityBot
- 1
3
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0
answers
106
views
The commutation relations of photon and gluon?
In QED, the photon field has the following commutation relations:
\begin{equation}
[A^{\mu}(t,\vec{x}),A^{\nu}(t,\vec{y})]=0, \tag{1}
\end{equation}
where $A^{\mu}(t,\vec{x})$ is the photon filed. ...
- 85
3
votes
1
answer
287
views
Time-evolution operator in QFT
I am self studying QFT on the book "A modern introduction to quantum field theory" by Maggiore and I am reading the chapter about the Dyson series (chapter 5.3).
It states the following ...
- 73.8k
-1
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39
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How to get $ H=\int\widetilde{dk} \ \omega a^\dagger(\mathbf{k})a(\mathbf{k})+(\mathcal{E}_0-\Omega_0)V $ in Srednicki 3.30 equation?
We have integration is
\begin{align*}
H =-\Omega_0V+\frac12\int\widetilde{dk} \ \omega\Big(a^\dagger(\mathbf{k})a(\mathbf{k})+a(\mathbf{k})a^\dagger(\mathbf{k})\Big)\tag{3.26}
\end{align*}
where
\...
- 207k
11
votes
3
answers
636
views
Why can the time-ordered exponentials be brought to the right?
Having worked through almost all calculations in section 4.2 of Peskin & Schroeder's An Introduction to QFT, I still don't get why we can get to Eq. (4.31)
\begin{equation}
\langle\Omega|\mathcal{...
- 952
4
votes
0
answers
107
views
Canonical commutation relation in QFT
The canonical commutation relation in QFT with say one (non-free) scalar real field $\phi$ is
$$[\phi(\vec x,t),\dot \phi(\vec y,t)]=i\hbar\delta^{(3)}(\vec x-\vec y).$$
Is this equation satisfied by ...
- 207k
3
votes
0
answers
77
views
Application of Callias operator in physics
In his article "Axial Anomalies and Index Theorems on Open Spaces" C.Callias shows how the index of the Callias-type operator on $R^{n}$ can be used to study properties of fermions in the ...
- 6,744
2
votes
2
answers
351
views
Relationship between normal-ordered vacuum state and parity operator
In the paper "Operator ordering in quantum optics
theory and the development of Dirac’s
symbolic method" by Hong-yi Fan, as referenced in this question, the authors mention the property
$$:A:...
- 14.8k
2
votes
1
answer
628
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What's the difference in defining normal ordering as $:c c^\dagger:=c^\dagger c$ vs $:c^\dagger c:=c^\dagger c- \langle c^\dagger c \rangle$?
If I understood correctly there are two terms called normal ordering:
$:c c^\dagger: = c^\dagger c \hspace{.5cm}$so shifting all creation operators to the left and all annihilation operators to the ...
- 207k