A mathematical construct used to study the effect of applying two operators in succession.

learn more… | top users | synonyms (1)

7
votes
2answers
278 views

How to replace $T$-product with retarded commutator in LSZ formula?

I am reading Itzykson and Zuber's Quantum Field Theory book, and am unable to understand a step that is made on page 246: Here, they consider the elastic scattering of particle $A$ off particle $B$: ...
-1
votes
2answers
120 views

Proving that conservation of momentum doesn't apply to electron in H-atom

To prove that the conservation of linear momentum doesn't apply to electron in H-atom, is it sufficient to show that angular momentum operator ($\hat L$) and momentum operator ($\hat p$) do not ...
5
votes
1answer
157 views

Apparent spacetime dependence of creation and annihilation operators

I'm currently going through An Introduction to Quantum Field Theory by Hartmut Wittig I've stumbled upon. Having trouble with equation (2.29), I'm asking the question: Do creation and annihilation ...
1
vote
1answer
47 views

Why is it “disconcerting” if the components of an operator do not commute?

A symmetrized operator is given by $$\hat{R}=\frac{1}{2\hat{H}}\hat{N}+\hat{N}\frac{1}{2\hat{H}}.$$ With $\hat{H}$ the Hamiltonian and $\hat{N}$ the first moment of energy. The defined $\hat{R}$ is ...
0
votes
1answer
32 views

Mutually Commutative

What is the definition of a Mutually Commutative set of operators? I've found articles describing a complete set of mutually commutative operators, but I can't actually find what mutually commutative ...
5
votes
0answers
107 views

Commutator as a time-ordered product

I'm reading through Seiberg and Witten's paper "String Theory and Noncommutative Geometry," and one part in $\S$2.1 isn't quite clear to me. (Sorry, in advance, for the length.) My question is about ...
4
votes
0answers
85 views

Do commutation relations exist between superfields?

To quantize a theory, Klein gordon field for example, commutation relations are stablished. Or anticommuting ones in the fermionic case. If I have the Wess.Zumino model or the free model: ...
3
votes
0answers
114 views

Virasoro Operators commutation relations

For the commutation relation in quantising the bosonic string $\left[L_n,L_{m}\right]=(n-m)L_{n+m}+\frac{D}{12}n(n^2-1)\delta_{n+m,0}$ we can then calculate this for $m=-n$ in between the vacuum ...
2
votes
0answers
104 views

Spinor Commutator in Peskin and Schroeder

In (3.87, page. 53) Peskin and Schroeder write $$\psi(\vec{x}) = \int\frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2E_{\vec{p}}}} e^{i\vec{p} \cdot \vec{x}} \sum_{s=1,2} (a_{\vec{p}}^{s}u^{s}(\vec{p}) + ...
2
votes
0answers
117 views

Commutators with function

I have following exercise: If $[C,D]$ is a c-number and $f(x)$ is a well-behaved function (i.e. all derivatives exist and are finite), show that: $$[C, f(D)]=[C,D]f'(D)$$ where $f'(D) = ...
2
votes
0answers
78 views

commutator to entropy in an uncertainty relationship?

Question: Does there exist a commutator to entropy in an uncertainty relationship? Similar Energy and time for instance.
2
votes
0answers
249 views

The correspondence between Poisson bracket and Commutators in Quantum Mechanics

I don't understand canonical quantization. In passing from classical to quantum, one replaces the Poisson brackets with the commutators. I don't really understand this. How can we generally show that ...
1
vote
0answers
52 views

Simultaneous eigenket

J. J. Sakurai states in his "Modern Quantum Mechanics", this fact as a theorem ($\pi$ is the parity operator): Suppose $$[H,\pi]=0$$ and $| n>$ is a nondegenerate eigenket of $H$ with ...
1
vote
0answers
38 views

Do the norms of the total and the orbital angular momentums commute? If yes, why is there a problem with 2p_{1/2}?

Question: For $\vec L$ the orbital angular momentum of an electron, $\bar S$ its spin, and $\vec J:=\vec L+\vec S$ the sum, do $\vec J^2$ and $\vec L^2$ commute? I assume it does: $[\vec J^2,\vec ...
1
vote
0answers
68 views

Why is commutation relations the first step in quantization?

Why is commutation relations the first step in quantization?
1
vote
0answers
64 views

How does linearity of a measurement imply that the commutator of all measured observables are $c$-numbers?

I really don't understand with the linearity conditions I have where this comes from.
1
vote
0answers
132 views

Commutator problem

I am trying to calculate the following commutator $$[\mathcal{H}_0(r',t'),\psi(r,t)]_-$$ where $\mathcal{H}_0 = (\frac{1}{2m}\nabla^2 + e\mathbf{A}(r',t'))^2 + e\phi(r',t') - \mu$, and $\mu$ is the ...
1
vote
0answers
58 views

commutators in an uncertainty relationship derived from a partition function?

The maximum information principle for the discrete case gives rise to a partition function (>>> see details here) $$Z(\lambda_1,\ldots, \lambda_m) = \sum_{i=1}^n \exp\left[\lambda_1 f_1(x_i) + \cdots ...
1
vote
0answers
145 views

QFT basics for Klein-Gordon fields

I am teaching myself QFT from Peskin for next years maths course and I have two questions: What is a c-number? Is it a complex number, and if so why does it mean, ...
0
votes
0answers
28 views

Commutator for time?

I know that in quantum mechanics, we can define space as the operator $\hat{x}=i\hbar \frac{d}{dp}$ in momentum space,and that position does not commute with momentum. However, in general relativity, ...
0
votes
0answers
93 views

QM: Commutation relations between irreducible vectors and angular momentum $[J^2,T_q^k]$

reading about the irreducible tensors and its commutation relations with the angular momentum one can find relations for $J_{z}$, $J_{+}$, $J_{-}$, but I was wondering, what about $J^2$ ? from ...
0
votes
0answers
112 views

Change of QM Momentum operator under coordinate transformation

Can any one please let me know what is the general procedure to construct the momentum operator under some coordinate transformation? For example, I understand that if ...
0
votes
0answers
143 views

Quantum Hamiltonian commuting with the Pauli-Runge vector

I have to prove that $[A_j, H] = 0$, with; $$\vec{A} = \frac{1}{2Ze^{2}m}(\vec{L} \times \vec{P} - \vec{p} \times \vec{L}) + \frac{\vec{r}}{r}$$ $$H = \frac{p^2}{2m} - \frac{Ze^2}{r}$$ And, $Z, e, ...