All Questions
9 questions
0
votes
2
answers
59
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Help with Commutators [closed]
I'm trying to self study quantum mechanics and am having a little trouble manipulating commutators. I get two different answers below, depending on the method I'm using. The second method gives me the ...
- 81
0
votes
0
answers
28
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Evaluating the commutator of derivative and position [duplicate]
In Zettili's book on quantum, the fully worked problem 2.6 asks to show
$$
\hat{A} = i(\hat{X}^2+1)\frac{d}{dx} + i\hat{X}.
$$
Is Hermitian. Where $\hat{X}$ is the position operator. I took the ...
0
votes
1
answer
242
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Commutator between covariant derivative and a field
I have field as an element of a Lie algebra as $\Phi = \phi^at^a$ and I want to calculate the commutator $$[D_{\mu}, \Phi],$$
with $$D_{\mu} = \partial_{\mu} + igA^a_{\mu}t^a,$$ the covariant ...
- 43
0
votes
2
answers
123
views
Ambiguity in Notation for Operators in Quantum Mechanics
Let's say I am trying to find the commutator of operators $\mathbf{A}$ and $\mathbf{B}$, and I get
$$[\mathbf{A},\mathbf{B}]=\nabla^2 f(x,y,z).\tag{0}$$
There seems to be some ambiguity here.
In ...
3
votes
0
answers
546
views
Commutation relation of four vectors [closed]
I was trying to prove that: $$[P_\mu, J_{\rho \sigma}] = i(\eta_{\mu \sigma} P_\rho - \eta_{\mu \rho} P_\sigma) $$
$\textbf{Attempt}$
$$\begin{align}
[P_\mu, J_{\rho \sigma}] = [P_\mu, x_\rho P_\sigma ...
- 1,327
0
votes
1
answer
1k
views
Commutator of covariant derivative and field $F_{\mu \nu}$
I am working with the covariant derivative and trying to show that the commutator of this derivative
$[D_\mu , D_\nu]$ is proportional to the field $F_{\mu \nu}$. That is, I need the final term to
be ...
user276724
1
vote
2
answers
228
views
Commutation of position four-vector with spacetime derivatives
I am trying to understand a simple demonstration in Ashok Das' Lectures in QFT. He does the following on p. 134
$$[P_\mu,M_{\nu\lambda}]=[\partial_\mu ,x_\nu\partial_\lambda-x_\lambda\partial_\nu]=\...
- 558
2
votes
1
answer
425
views
Question about commutators acting on wavefunctions
Consider a commutator acting on a 1D wavefunction:
$$[\frac{\hbar}{i} \frac{d}{dx},x]\psi(x)=(\frac{\hbar}{i} \frac{d}{dx}x-x\frac{\hbar}{i} \frac{d}{dx})\psi(x).$$
Now does this mean
$\frac{\hbar}{...
- 4,276
0
votes
2
answers
637
views
Notation and concepts of Yang Mills Theory
I am studying loop quantum gravity using the book by Pullin and Gambini. I am having some trouble understanding and getting past the chapter on Yang Mills theory, mainly because I am confused about ...
- 103