All Questions
Tagged with quantum-field-theory hilbert-space
681
questions
45
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3
answers
4k
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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
38
votes
4
answers
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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
35
votes
1
answer
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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
30
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4
answers
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What is the meaning of a state in QFT?
I guess this may be more of a mathematical than a physics question, but it comes down to physical interpretations, so I'm posting it here.
In classical Quantum Mechanics, we can define a state $\left|...
- 1,106
25
votes
4
answers
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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
25
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2
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In what sense is the path integral an independent formulation of Quantum Mechanics/Field Theory?
We are all familiar with the version of Quantum Mechanics based on state space, operators, Schrodinger equation etc. This allows us to successfully compute relevant physical quantities such as ...
- 2,212
25
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3
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The Origins of the Second Quantization
I've been studying quantum theory for a while now and have a number of closely related questions that are not giving me any peace. I am not sure if such a long format is appropriate here, but I'd like ...
- 2,921
24
votes
1
answer
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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
23
votes
5
answers
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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
23
votes
1
answer
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The vacuum in quantum field theories: what is it?
In Section 10.1 of his textbook Quantum Field Theory for Mathematicians, Ticciati writes
Assuming that the background field or classical source $j(x)$ is zero at space-time infinity, the presence ...
- 8,540
21
votes
1
answer
912
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How can a Hamiltonian determine the Hilbert space?
Sometimes, when discussing quantum field theory, people speak as if a Hamiltonian determines what the Hilbert space is. For example, in this answer AccidentalFourierTransform says
Imagine an $H_0$ ...
- 103k
21
votes
1
answer
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Unitary quantum field theory
What do physicists mean when they refer to a quantum field theory being unitary? Does this mean that all the symmetry groups of the theory act via unitary representations? I would appreciate if one ...
- 415
20
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2
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Hilbert Space of (quantum) Gauge theory
Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something ...
user32229
20
votes
1
answer
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What is an observer in QFT?
In non-relativistic quantum mechanics, an observer can be roughly describe as a system with wavefunction $\vert \psi^O \rangle$ which, upon interaction with another system $\vert \psi^S\rangle$ (in ...
- 16.5k
18
votes
3
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Meaning of Fock Space
In a book, it says, Fock space is defined as the direct sum of all $n$-body Hilbert Space:
$$F=H^0\bigoplus H^1\bigoplus ... \bigoplus H^N$$
Does it mean that it is just "collecting"/"adding" all ...
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