All Questions
Tagged with quantum-field-theory hilbert-space
137
questions
24
votes
1
answer
3k
views
Getting particles from fields: normalization issue or localization issue?
There seems to be something very strange about the relationship between quantum field theory and quantum mechanics. It is bothering me; perhaps somebody can help.
I'll consider a free Klein-Gordon ...
- 884
13
votes
1
answer
5k
views
Time-ordering vs normal-ordering and the two-point function/propagator
I don't understand how to calculate this generalized two-point function or propagator, used in some advanced topics in quantum field theory, a normal ordered product (denoted between $::$) is ...
- 9,581
38
votes
4
answers
5k
views
Scattering, Perturbation and asymptotic states in LSZ reduction formula
I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix ...
- 26.8k
23
votes
5
answers
11k
views
Why is normal ordering a valid operation?
Why is normal ordering even a valid operation in the first place? I mean it can give us some nice results, but why can we do the ordering for the operators like that?
Is its definition motivated by ...
- 2,301
14
votes
2
answers
5k
views
Position operator in QFT
My Professor in QFT did a move which I cannot follow:
Given the state $$\hat\phi|0\rangle = \int \frac{d^3p}{(2\pi)^3 2 E_p} a^\dagger_p e^{- i p_\mu x^\mu}|0\rangle,$$ he wanted to show that this ...
- 263
16
votes
2
answers
4k
views
Boosts are non-unitary!
Unlike rotations, the boost transformations are non-unitary. Therefore, the boost generators are not Hermitian. When boosts induce transformations in the Hilbert space, will those transformation be ...
- 26.8k
45
votes
3
answers
4k
views
What is the issue with interactions in QFT?
I've started studying QFT this year and in trying to find a more rigorous approach to the subject I ended up find out lots of people saying that "there is no way known yet to make QFT rigorous when ...
- 36.4k
12
votes
1
answer
765
views
Conceptual difficulty in understanding Continuous Vector Space
I have an extremely ridiculous doubt that has been bothering me, since I started learning quantum mechanics.
If we consider the finite dimensional vector space for the spin$\frac{1}{2}$
particles, ...
- 379
5
votes
2
answers
1k
views
The use of $a^\dagger(\mathbf{k}) = -i \int d^3x e^{ikx}\stackrel{\leftrightarrow}{\partial}_0 \phi(x)$ in the derivation of the LSZ-formula
I noticed that in Srednicki's derivation of the LSZ-formula the expression (chapter 5) for the creation (and also later for the annihilation) operator by the field operator:
$$a^\dagger(\mathbf{k}) = -...
- 9,778
35
votes
1
answer
5k
views
What really are superselection sectors and what are they used for?
When reading the term superselection sector, I always wrongly thought this must have something to do with supersymmetry ... DON'T laugh at me ... ;-)
But now I have read in this answer, that for ...
- 9,581
25
votes
4
answers
2k
views
Separability axiom really necessary?
I know other people asked the same question time before, but I read a few posts and I didn't find a satisfactory answer to the question, probably because it is a foundational problem of quantum ...
- 491
13
votes
4
answers
3k
views
Path integral derivation of the state-operator correspondence in a CFT
Below, I paraphrase the path integral derivation of the state-operator correspondence in chapter 4 of David Tong's string theory notes (see pdf here). This is my interpretation of the text in that pdf,...
- 26.6k
16
votes
1
answer
8k
views
Klein-Gordon inner product
Studying the scalar field and Klein-Gordon equation in quantum field theory I came across this definition for the inner product in the space of the solutions of the K.G. equation:
$$\langle \Phi_1 | \...
- 271
11
votes
1
answer
2k
views
Fock space vs. wavefunctionals
There are at least two representations of the Hilbert spaces of quantum field theory. For a scalar field, we have
The Fock space representation, such that every state is represented as the Fock ...
- 16.5k
9
votes
2
answers
2k
views
What is intuitive or physical meaning of wave functional and field configuration and field eigenfunction?
what is the physical meaning of field configuration in quantum field theory. I have come across such terminologies in Schrodinger field theory and path integral field theory. What is the actual ...
- 1,068