All Questions
99
questions
0
votes
2
answers
116
views
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
votes
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
-1
votes
0
answers
39
views
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
\...
- 37
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 ...
- 2,226
1
vote
0
answers
43
views
Conjugate momenta in Radial Quantization
When we radially quantize a conformal field theory, is there at least formally a notion of a conjugate momentum $\Pi$ to the primary fields $O$ which would satisfy an equal radius commutation relation ...
- 482
2
votes
0
answers
37
views
Double Discontinuity In CFT
In the paper Analyticity in Spin in Conformal Theories Simon defines the double discontinuity as the commutator squared in (2.15):
$$\text{dDisc}\mathcal{G}\left(\rho,\overline{\rho}\right)=\left\...
- 194
0
votes
0
answers
35
views
Lorentz invariance (LI) of time ordering operation
At Srednicki after eq. (4.10), we have a discussion about that the time ordering operation. Have to be frame inv. I.e it has to be LI.
He wrote that for timelike separation we don't have to worry ...
1
vote
1
answer
94
views
Why does we quantize fields $\phi(t,x)$ and not $\phi$?
In classical mechanics, the action of a theory is determined by its Lagrangian:
$$S(q) := \int L(q(t),\dot{q}(t),t)dt $$
In the following, let us assume that $L$ does not depend explicitly on time. ...
- 1,131
0
votes
0
answers
63
views
Questions about computing the commutator of the Lorentz generator
I am computing the commutator of the Lorentz generators, from the Eqn (3.16) to Eqn (3.17) in Peskin & Schroeder.
$$
\begin{aligned}
J^{\mu\nu} &= i(x^\mu \partial^\nu - x^\nu \partial^\mu ) &...
- 41
2
votes
2
answers
132
views
Commutator of conjugate momentum and field for complex field QFT
In Peskin & Schroeder's Introduction to QFT problem 2.2a), we are asked to find the equations of motion of the complex scalar field starting from the Lagrangian density. I want to show that:
$$i\...
- 538
0
votes
0
answers
63
views
Action of Conjugate momentum $\hat{\pi}$ on $\hat{\phi}$ eigenstate [duplicate]
So I am trying to solve ex. 14.3 in Schwartz textbook "Quantum Field Theory and the Standard Model"
and in the second requirement, he wanted me to show that the action of the conjugate ...
2
votes
2
answers
314
views
CFT Radial Quantization Raising and Lowering Operators Sign Question [closed]
Following Slava Rychkov (Page 41, Or here on arxiv page 39), I am trying to show that the momentum operator raises the scaling dimension.
I've seen the other related questions on this matter by Y. ...
- 194
3
votes
1
answer
126
views
Dressing an operator by Wilson line in Quantum Electrodynamic
I am reading a paper arXiv:1507.07921 which introduce gravitational dressing. The paper compare it to dressing in QED.
Consider the scalar QED lagrangian
$$\mathcal{L}=-\frac{1}{4}(F^{\mu\nu})^2-|D_\...
- 133
1
vote
1
answer
84
views
A simple question on creation and annihilation operators
We know that the KG solution for a Spin-0 particle has the following Hamiltonian
$$\hat{H}=∫ d^{3}p\frac{ω_{p}}{2}(\hat{a}_{p}\hat{a}^{\dagger}_{p}+\hat{a}^{\dagger}_{p}\hat{a}_{p})\hspace{2cm}[\hat{a}...
- 477
0
votes
1
answer
107
views
Commutator of annichilation and creation operators [closed]
Let $\phi$ be a real scalar field and $\psi$ a complex scalar field. Therefore, we can expand $\phi$ in terms of $a_{\boldsymbol{p}}, a^\dagger_{\boldsymbol{p}}$ and $\psi$ in terms of $b_{\boldsymbol{...
- 357