All Questions
29
questions
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What determines the conjugation of a state in quantum field theory?
In basic quantum mechanics, we define the inner product between two states $\phi$ and $\psi$ as $\phi^\dagger \psi$, where $\phi^\dagger$ is the conjugate transpose of the vector $\phi$. However in ...
- 2,504
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0
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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
1
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1
answer
165
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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 ...
- 619
2
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167
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Unitary representations of a Lorentz transformation
In QFT we have an action of the restricted Lorentz group which is implemented via a unitary transformation. In other words, if $\Lambda\in SO(1,3)^\uparrow$, then the corresponding unitary operator is ...
- 145
8
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1
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337
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Normal ordering and construction of the physical Hilbert space
In Ref. 1 the author states:
The procedure of normal ordering allows us to define the physical Hilbert space. The physical meaning of this approach becomes more transparent in the thermodynamic limit ...
- 8,094
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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
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1
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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
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2
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75
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Does the location of the Hilbert space of momentum eigenstates in QFT change under time translations and boosts?
I have two questions concerning Wigner's transformation law for irreps of the Poincare group:
\begin{equation}
U[\Lambda,\vec{a}]\vert p,\sigma\rangle=e^{ip\cdot a}D_{\sigma'\sigma}[\Lambda;p]\vert \...
- 2,270
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
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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 ...
1
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1
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297
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Wigner's symmetry representation theorem and representations of the homogeneous Lorentz group
In Weinberg's QFT textbook (volume 1), he proved the symmetry representation theorem in Appendix A, chapter 2, which states
Any symmetry transformation can be represented on the Hilbert space of ...
- 69
3
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1
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652
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Lorentz transformation: unitary $U(\Lambda)$ on the state of the Hilbert space, but the boost $\Lambda_{1/2}$ is not unitary on $\psi$
In p.59 of Peskin and Schroeder QFT book, he mentioned that
the operator $U(\Lambda)$ that implements the Lorentz transformations on the state of the Hilbert space is unitary, even though the boost $\...
- 4,336
4
votes
2
answers
196
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Why is it useful to characterize relativistic particle states by this kind of wavefunction?
This question is a followup to my previous one "Why are momentum eigenstates in QFT plane waves?
" as it made sense for me to ask this separately, in a self-contained manner.
In QFT we have ...
user303517
11
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1
answer
884
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Why are momentum eigenstates in QFT plane waves?
In Weinberg's The Quantum Theory of Fields, Chapter 2, he works out the Wigner classification of the unitary representations of the Poincare group. In particular, one finds that the possible one-...
user303517
5
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1
answer
440
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Weinberg QFT vol 1, chapter 2. On symmetries in QM and the universal cover
While reading chapter 2 of the book Quantum theory of fields: Volume 1 of Weinberg I got pretty much confused. All the confusion starts in page 89 with equation 2.7.43 and 2.7.44:
$$
U(\Lambda) U(\bar\...
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