All Questions
25
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About momentum states covariant normalization
I'm following QFT of Schwrtz and I have a doubt about Eq. (2.72).
In particular, from Eq. (2.69): $$[a_k,a_p^\dagger]=(2\pi)^3\delta^3(\vec{p}-\vec{k}),\tag{2.69}$$ and Eq. (2.70): $$a_p^\dagger|0\...
- 147
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1
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106
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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 ...
- 43
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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.
...
- 21
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89
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Why Lorentz transf. representation in spin 1/2 particles Hilbert space is not a unitary operator? [duplicate]
Weinberg introduces the idea of Lorentz group representation describing how vectors in the Hilbert space of definite momentum states should change due to a L.T. It is understandable that to preserve ...
2
votes
1
answer
161
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How is there a conflict between unitarity and Lorentz invariance?
I've read a paragraph in Schwartz-QFT where he argues that unitarity and Lorentz invariance are incompatible due to the norms being different:
Why does he assume that the boost in this basis is $(\...
- 1,477
2
votes
2
answers
163
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Srednicki's QFT: Why $\langle p|\phi(0)|0\rangle$ in the interacting theory is Lorentz invariant?
I am reading Srednicki's QFT and I have met a problem. In its section 5, (5.18) , after deducing the LSZ formula, in order to check whether his supposition "that the creation operators of free ...
- 125
2
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0
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137
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Why do we need a whole field of operators in QFT?
This is probably a very silly question, so I hope you'll excuse my ignorance of QFT. As far as I can tell, there are really two mathematical objects in the Hamiltonian formulation:
The state vector, ...
- 2,475
3
votes
1
answer
223
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What makes coming up with a mathematically solid, non-shaky relativistic quantum field theory (RQFT) so hard?
This is something I know of but I'm not quite sure I understand the details. Particularly, when it comes to interacting RQFTs, such as even QED, where some posts here have pointed out that it cannot ...
- 20.6k
1
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133
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If the scattering amplitudes are Lorentz scalars, why is S-matrix Lorentz covariant?
All observers should agree on the probabilities: $\mathcal{P}(\mathcal{R}_1 \rightarrow \mathcal{R}_2)$ in an inertial frame $\mathcal{O}$ = $\mathcal{P}(\mathcal{R}_1' \rightarrow \mathcal{R}_2')$ ...
- 433
3
votes
2
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647
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Lorentz transformation of annihilation operator
In Srednicki's Quantum Field Theory, chapter 4, the author claims that the Lorentz transformation for given a scalar field $\varphi(x)$,
\begin{align}
U(\Lambda)^{-1} \varphi(x) U(\Lambda) = \varphi(\...
- 1,540
3
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0
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137
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Reasoning for projective representations of Lorentz group in the context of QFT
As far as I understand from posts such as this and this, when determining what is possible in a relativistic theory, Wigner's theorem tells us that we care about objects transforming under projective ...
- 737
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0
answers
161
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Obtaining the unitary representation of the Lorentz group from infinitesimal transformations
My knowledge of Lie Groups and Lie Algebras is very limited, even more so when it comes to their representation theories. There is a difference that I can't quite understand, between the ...
0
votes
2
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394
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Needs of unitary representation for QFT
Weinberg book states the following (pg. 231):
"There is no problem in working with non-unitary representations, because the objects we are now concerned with are fields, not wave functions, and ...
- 613