All Questions
Tagged with quantum-field-theory hilbert-space
681
questions
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How does Weinberg definition of particle states from standard momentum work?
In his first volume, part 2.5, Weinberg define one particle states $Φ_{p,𝜎}$ ($p$ is the momentum and $𝜎$ another quantum number) in the following way :
Choose a Standard momentum $k$
Find a ...
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93
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How do Poincare group act on Classical field, Quantum field operator, Field configuration states, Fock space states?
I will try to make each of my statement as clear as possible, if any of the statements are wrong prior to my question, please point them out:)
For simplicity, we work in free QFT with scalar field.
...
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Dimensionality of state space of TQFTs
As the title suggests, I am wondering about the dimensionality of state spaces in $d$-dimensional TQFTs. As of yet I have mostly been concerned with the mathematical, functorial definition of TQFTs as ...
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Concrete understanding of QFT Hilbert space for spinor
I'm trying to understand the concepts of a spinor field in QFT. I naively understand there are two values at each spatial position $\vec{r}$: a probability amplitude and a spinor value. Is there a ...
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What physical processes other than scattering are accounted for by QFT? How do they fit into the general formalism?
For background, I'm primarily a mathematics student, studying geometric Langlands and related areas. I've recently been trying to catch up on the vast amount of physics knowledge I'm lacking, but I've ...
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What is the single-particle Hilbert space in the Fock space of QFT?
In Quantum field theory, the fields are operator-valued functions of spacetime. So for a scalar (spin $0$) field $$\psi: \mathbb{R}^{3,1} \rightarrow O(F),$$ where $O(F)$ is the space of operators on ...
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How is the Wigner little group representation of Poincaré group Unitary?
From Weinberg's QFT Vol.1, eq(2.5.11):
$$U(\Lambda)\Psi_{p,\sigma}=({N(p)\over N(\Lambda p)})\sum_{\sigma'}D_{\sigma'\sigma}(W(\Lambda,p))\Psi_{\Lambda p ,\sigma '}.\tag{2.5.11}$$
However, this is not ...
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Calculation about fermions via quantum field theory
I want to ask a specific question occurred in my current learning about neutrinos.
What I want to calculate is an amplititude:
\begin{equation}
\langle\Omega|a_{\bf k m}a_{\bf pj}a_{\bf qi}^{\dagger}...
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1
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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.
...
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115
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Quantum field theory states
I've been told that in QFT, everything is turned into their continuum type, i.e:
$$q_i \to \phi(x)$$
$$p_i \to \pi(x)$$
$$[q_i, p_j] = i\delta_{ij} \to [\phi(x), \pi(y)] = i\delta(x-y)$$
etc.
Now I've ...
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1
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The wave-function in QFT
As I understand, the wave-function in QFT becomes a wave-functional dependent on fields. I have heard this told by Sean Carroll in his Biggest Ideas in the Universe lectures. Srednicki gives the $n$-...
- 525
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What is the definition of bound state in quantum field theory?
I asked a question a while a go what is a bound state and the question was closed because there is a similar question.
Now since best description we have to describe nature in quantum field theory
How ...
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An issue with spectral representation in Coleman's proof of Goldstone's theorem in his Lectures on QFT
I am working through the proof of Goldstone's theorem in Coleman's Lectures on QFT in chapter 43.4.
He uses a Källén-Lehmann-like spectral representation of
$$\langle 0 | j_{\mu}\left(x\right)\phi\...
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