All Questions
23
questions
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Lorentz transformation of Creation and Annihilation operators for a real scalar field theory - MIT OCW QFT I Problem set 3 [closed]
I have been working through the MIT OCW's QFT lecture notes and problem sets, but I have come to realize that I have a fundamental misunderstanding of what is meant by how objects transform under ...
6
votes
1
answer
142
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SUSY and the BMS group
I'm watching this intro to Supersymmetry lecture by Nathan Berkovits and, at roughly 33 minutes, he mentions he is going to extend the Poincaré group in an essentially unique manner, where "...
- 22.1k
2
votes
0
answers
61
views
Poincaré with spontaneously broken translations
What is the physical interpretation of Poincaré symmetries with spontaneously broken spatial and temporal translations?
Is there an interesting low-energy effective model for it and what are its ...
- 1,354
-1
votes
1
answer
161
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Is the Standard Model, in some sense, special relativity plus everything possible?
I found this intro to QFT on YouTube really helpful (and apparently I'm not the only one). Let my try to summarize it:
We start with Minkowski space. We want to add a field to it, but there are only ...
- 2,475
2
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0
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84
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Are canonical commutation relations only valid for non-relativistic QM? [closed]
Other questions (such as What is the "secret " behind canonical quantization?) seem to suggest that ultimatley, the motivation behind imposing the canonical commutaiton relation $$[x,p]=i\...
- 2,604
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2
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223
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How can we show the Lorentz symmetry is not anomalous in $\phi^{4}$ theory?
how can I show in a lagrangian with scalar fields and $\phi^{4}$ interaction, the energy-momentum tensor isn't anomalous?
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1
vote
1
answer
97
views
Matrix element of the currents associated with the broken generators between the vacuum and Goldstone's bosons
Let $G$ be a Lie group and $L^i$ the generators of this group. Suppose we have $L^{j}|0\rangle \neq 0$ where $|0\rangle \neq 0$ denotes the vacuum. If $G$ is associated with a symmetry of the ...
- 445
2
votes
1
answer
193
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What do we mean by saying product of operators is a scalar?
The motivation for this question is considering the helicity of a massless particle in relativistic QFT.
As the definition for helicity operator $h$
$$
h=\frac{\mathbf{J} \cdot \mathbf{P}}{|\mathrm{P}|...
- 503
8
votes
2
answers
3k
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What is the exact meaning of Lorentz invariance for a quantum scalar field?
In axiomatic QFT, the defining property of a scalar field $\phi$ is that it does not change under a Lorentz transformation: that is, "If $U(\Lambda)$ is the unitary representation of a Lorentz ...
- 596
5
votes
1
answer
357
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How does preservation of the Lorentz algebra demonstrate Lorentz invariance of a QFT?
In his book "Quantum Field Theory of Point Particles and Strings", Brian Hatfield makes the following claim (on p. 46) after canonically quantizing the free scalar field theory:
We started with a ...
- 98
1
vote
1
answer
553
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Why can we associate the rotation operator for a vector field to the angular momentum operator?
I've seen the operator that rotates a scalar field and its properties. Considering that the wave function of a particle (if I don't consider the spin) is described by a scalar field and that this ...
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1
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105
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Do Lorentz invariance and General covariance always hold at low energies, or are they sometimes violated?
This is motivated by Weinberg’s folk theorem, where the construction of our perturbative expansion (and choice of theory space) is mostly safe given that we only have to enforce very general symmetry ...
- 13
4
votes
1
answer
185
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Weinberg's Coleman-Mandula theorem proof sufficient condition for isomorphism?
In Weinberg's QFT Volume 3 book on Supersymmetry, he presents his own proof of the Coleman-Mandula theorem. As part of the proof, he proves that the only possible internal symmetry generators must ...
- 3,514
1
vote
1
answer
234
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Why do we not require physical laws to be invariant under the action of a bigger transformation group?
In Quantum Field Theory, Lagrangians are constructed such that the coordinates on which the quantum fields depend are invariant under action of the Poincare group $\mathbf{P}(1,3):=\mathbf{R}^{(1,3)} \...
- 234
4
votes
2
answers
633
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Are all forms of "charge" Lorentz invariant?
Electric charge is Lorentz invariant (as shown in this question). Are weak isospin and color charge also Lorentz invariant quantities? My intuition says that they should be, but I've never seen any ...
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