All Questions
134
questions
3
votes
0
answers
57
views
Is there any difference between Wick time order and Dyson time order?
Reading A Guide to Feynman Diagrams in the Many-Body Problem by R. Mattuck, I am getting the feeling that I missed something subtle related to time order. When deriving the Dyson series for the ...
- 5,578
0
votes
2
answers
88
views
Ladder operators and creation & annihilation operators - different between $a$, $b$ and $c$ [closed]
Usually, the ladder operator denoted by $a$ and $a^\dagger$. In some case, people talk about the creation operator and denote it by $c$ and $c^\dagger$. Recently I see another notation, $b$ and $b^\...
- 23
2
votes
0
answers
113
views
Confused about square of time-reversal operator $T$
I am reading An Introduction to Quantum Field Theory by Peskin & Schroeder, and I am confused about what is the square $T^2$ of time reversal operator $T$.
My guess is that for $P^2$, $C^2$ and $T^...
- 613
6
votes
4
answers
623
views
How can a QFT field act on particle states in Fock space?
Recently I asked a question that was considered a duplicate. However I felt that the related question didn't answer my doubts. After a bit of pondering I have realized the core of my discomfort with ...
- 4,577
3
votes
3
answers
815
views
Transition from position as operator in QM to a label in QFT
In David Tong's lecture "Quantum Field Theory" - Lecture 2, he said that
"In Quantum mechanics, position is the dynamical degree of the particle which get changed into an operator but ...
user385554
1
vote
2
answers
188
views
Squared spin operators in second quantization
Spin operator in second quantization can be written as:
\begin{equation}
\hat{\vec{S}}_{i} = \frac{1}{2} \sum_{\sigma \sigma'} \hat{c}^{\dagger}_{i\sigma} \hat{\vec{\sigma}}_{\sigma \sigma'} \hat{c}_{...
- 13
5
votes
2
answers
629
views
Time ordering operator identity
In Ref. 1, the author states that:
Making use of the fact that in a chronological product factors with different time arguments on the path $C$ may be commuted freely, application of the group ...
- 8,094
2
votes
2
answers
214
views
Gibbs state and creation and annihilation operators
Let's consider quantum Fermi or Bose gas. Let $a(\xi)$, $a^{\dagger}(\xi)$ are standard annihilation and annihilation operators. Hamiltonian of system is denoted as
$$
\hat{H} = \int_{R^3} \frac{p^2}{...
- 33
2
votes
1
answer
143
views
How is a Fock state from QFT related to the wave function from quantum mechanics?
I am currently studying quantum field theory as part of my degree. I'm just lacking intuition or an understanding of some basic concepts. So please don't hesitate to correct me if i got something ...
- 29
1
vote
0
answers
73
views
Convergence of series of elements in a quasi-local algebra
I am studying the quasi-local algebra on Bratteli and Robinson Operator Algebras and Quantum Statistical Mechanics, but there is one thing that is not clear to me at the moment. Let's say that the ...
- 159
0
votes
0
answers
56
views
Adjoint of the Dirac equation, and hermiticity of the momentum operator
I'm trying to derive the adjoint of the Dirac equation in standard relativistic quantum mechanics. We have the Dirac equation as follows :
$$(i\gamma^{\mu}\partial_\mu -m)\psi=0$$
To find it's adjoint,...
- 1,791
1
vote
0
answers
34
views
Normalisation for a two fermion state
I'm trying to follow this paper (Fermion and boson beam-splitter statistics. Rodney Loudon. (1998). Phys. Rev. A 58, 4904)
However, I don't quite understand where some of his results come from.
...
- 33
1
vote
0
answers
46
views
Von Neumann Algebra decomposition
I am trying to understand the Von Neumann decomposition, according to which every Von Neumann Algebra can be uniquely decomposed as integral (or direct sum) of factors. More specifically, I am trying ...
- 159
3
votes
0
answers
101
views
Properties and physical meaning of disjointness of reducible representations
I have the following doubt. Let's assume we have two mixed states $\rho_1 = \Sigma_i a_i \omega_i^{1}$ and $\rho_2 = \Sigma_i b_i \omega_i^{2}$ on the same algebra, where the states $\omega$ are all ...
- 159
2
votes
1
answer
119
views
Understanding mathematically the promotion of field/observable to operator in QFT
First, I know it "worked", in physics sense.
My question is what happened in the math sense.
When promoting something, such as a field, to an operator, am I essentially mapping the field to ...
- 63