All Questions
Tagged with symmetry-breaking quantum-field-theory
431
questions
1
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34
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Goldstone Theorem in Schwartz, follow-up
This is somewhat of a related question to
Goldstone theorem in Schwartz
and is related to equation 28.16 in Schwartz's QFT book.
One way to prove that
$$ \langle \Omega | J^\mu(x) | \pi(p) \rangle = i ...
- 29
2
votes
1
answer
57
views
Alternative potentials in the context of spontaneous symmetry breaking
Consider a one-dimensional real scalar field $\phi$. Usually when spontaneous symmetry breaking (SSB) with such field is discussed, the following potential is assumed:
$$V=-\mu^2\phi^2+\lambda \phi^4$$...
- 88
0
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0
answers
50
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Simplified Explanation of Coleman-Weinberg Potential in QFT
I have been reading a research paper where the interaction potential between two scalar fields is given by $$=g\, \phi H^\dagger H .$$ The Coleman-Weinberg correction to the potential is: $$ \frac{n}{...
- 105
0
votes
0
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48
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Conformal invariance and mass terms in QFT
We know that a physically sensible QFT must be renormalizable. If I understand correctly, when this happens, the theory has "asymptotic freedom" and is conformally invariant past some high ...
- 407
6
votes
1
answer
148
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Goldstone theorem for classical and quantum potential
Consider a quantum theory $$\mathcal{L}(\phi^a) = \mathcal{L_{kin}}(\phi^a)-V(\phi^a),\tag{11.10}$$ depending on any type of fields $\phi^a$.
The VEV of this theory are constant fields $\phi_0^a$ such ...
- 305
3
votes
1
answer
95
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Are Higgs mechanism and SSB different phenomena?
In the Standard Model, the Higgs mechanism is associated with the Spontaneous Symmetry Breaking (SSB).
My understanding is that it is the Higgs field which breaks the $SU(2) \times U(1)$ symmetry at a ...
- 1,665
2
votes
0
answers
64
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Masses of $SU(2)$ gauge bosons
I'm currently learning quantum field theory and I'm wondering one thing.The way I understood it is that in the $SU(2)$ Yang-Mills theory, all gauge bosons have the same mass due to the spontaneous ...
- 41
5
votes
1
answer
909
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Higgs mechanism and mass gap in the Standard Model - asking for some clarification
Higgs mechanism is known to give "mass" to gauge bosons, especially in electroweak theory where the gauge group is given by $SU(2) \times U(1)$.
However, as in this PE post or the statement ...
- 1,665
1
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0
answers
37
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Loop Calculations of A Spontaneous Broken gauge theory with fermions
Let me first rephrase the background. Consider adding a massless fermion to the spontaneously broken $U(1)$ gauge theory through a chiral interaction:
$$
\mathcal{L}=\bar{\psi}_{L}i \gamma_{\mu}D^{\mu}...
- 81
1
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0
answers
36
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Does the changes of flow regimes of the renormalization group flow diagram imply always that a symmetry has been broken?
Usually we can use RG flow diagrams to understand that a phase transition has happened. Because they are intimately related to a broken symmetry, does that imply that it always implies that a symmetry ...
- 11
1
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2
answers
119
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Confusion about Higgs mechanism
I am trying to understand the mass acquisition of particles in the Standard Model based on the book 'Fundamentals of Neutrino Physics and Astrophysics' by C. Giunti, and several doubts have arisen ...
- 161
1
vote
1
answer
78
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What implements finite conformal transformations in two dimensions?
In a two dimensional conformal field theory I have two sets of generators giving a representation of the Virasoro algebra
$$L_n, \bar{L}_n, n \in \mathbb{Z}$$
$$[L_n,L_n] = (m-n) L_{m+n} + c\frac{m(m^...
- 420
0
votes
1
answer
54
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Why don't we include diagrams with fermion and gauge boson external lines while calculating the effective potential of Standard model?
While calculating the effective potential of Higgs boson, we aim at $V_{eff}(h)$ instead of $V_{eff}(h, W^{+}, W^{-}, Z, quarks, leptons)$. I think the true vacuum should be the minimum of this ...
- 619
0
votes
1
answer
58
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Can we prove in general that gauge fields associated with broken generators form representations of the unbroken group?
The title is a bit ambiguous. More specifically, I'm asking:
Are all coupling between massive gauge fields (associated with broken generators) and massless gauge fields of the unbroken group are in ...
- 619
1
vote
0
answers
48
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Calculation of Vertex factor from Lagrangian
I am studying spontaneous symmetry breaking of a complex scalar field $\phi(x)$ of a global $U(1)$ symmetry: $\phi(x)\to e^{i\alpha}\phi(x)$, where $\alpha$ is a real constant. I am considering the ...
- 35