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Results tagged with symmetry-breaking
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In explicit symmetry breaking, the equations of motion of a physical system are variant under the broken symmetry; by contrast, for spontaneous symmetry breaking (SSB), these equations are invariant, but the entire system is not because its vacuum (background) is non-invariant. Further use for the SSB characteristic nonlinear realizations (Goldstone mode), and the group theoretical patterns involved.
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Do expectation values of quantum fields behave like classical fields?
A famous result in quantum mechanics is Ehrenfest's theorem which states that the expectation values of observables are governed by the classical equations of motion.
Does a similar statement hold f …
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3
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1
answer
343
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Can a symmetry breaking VEV lie far above the "symmetry breaking scale?"
The scale where some symmetry gets broken can be computed using the renormalization group equations for the gauge couplings. If there is only one Higgs VEV responsible for some breaking, can this VEV …
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Breaking of a local symmetry is impossible, so what "discrete remnant global symmetry" is th... [duplicate]
Breaking of a local symmetry is impossible. It is often said that therefore the role of the Higgs mechanism in the standard model is a different one.
Namely,
Once a gauge is fixed, however, to r …
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1
answer
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Where do the Goldstone Boson degrees of freedom come from?
The punchline of Goldstone's theorem is well known. When a continuous symmetry breaks
necessarily, new massless (or light, if the symmetry is not exact) scalar particles appear in the spectrum of …
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0
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229
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Given a VEV how can I compute which generators remain unbroken using tensor methods?
This is a follow up to this question.
A generator $T_a$ of a given gauge group $G$ remains unbroken after some Higgs field $\Phi$ gets a vev if
$$ T_a \langle\Phi\rangle =0 $$
I'm trying to unders …
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2
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2k
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What happens to Goldstone bosons in the Higgs potential after symmetry breaking?
When the gauge symmetry of our Lagrangian breaks spontaneously through the Higgs mechanism, we usually find that $n$ Higgs degrees of freedom become massless through the vacuum expecation value (vev), …
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5
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1
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Do conservation laws still hold for spontaneously broken symmetries?
For a given gauge symmetry $G$, we get via Noether's theorem conservation laws
$$ \partial_\mu j^\mu = 0 . $$
Do these conservation laws still hold, when $G$ gets broken spontaneously through a no …
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1
answer
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Are Photons Goldstone Bosons?
I'm not interested in more speculative ideas, like the one of Bjorken et. al. that photons are Goldstones of broken Lorentz symmetry.
Instead, I want to understand if photons are simply the Goldston …
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2
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1
answer
463
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Why is there an infinite potential barrier between degenerate vacua in QFT?
I recently read "Fifty Years of Yang-Mills Theory and my Contribution to it" by R. Jackiw, and stumbled upon an intriguing sentence:
Usually in quantum field theory tunneling is suppressed by infi …
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1
answer
655
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Why do we assume the spatial volume is infinite?
So far, I thought that big bang scenario implies that spacetime is finite. It started at zero and now becomes bigger. In addition, at a minimum, we have a causal horizon and anything farther away shou …
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Why is a superposition of vacuum states possible in QCD, but not in electroweak theory?
There are two standard stories floating around in modern particle physics:
Spontaneous symmetry breaking can only happen in a QFT, like in the electroweak theory, because no tunneling between the de …
- 10.3k
3
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1
answer
201
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How to find the remaining subgroup after some linear combination of Higgs fields gets a VEV?
This is a follow-up question to this question.
How can I compute which generators remain unbroken when a linear combination of Higgs fields $a \Phi_1+ b\Phi_2$ get a vev?
If I compute the unbroken …
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1
vote
1
answer
402
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How to find the remaining subgroup after some Higgs field gets a VEV?
Say we have a group $G$ and a set of Higgs fields in a representation $R$ of $G$. One of the Higgs fields in $R$ gets a VEV, how can I determine the remaining subgroup after this symmetry breaking?
I …
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Resource for (String) Symmetry Breaking in Terms of Roots and Weights?
I'm currently searching, for quite a while now, for a paper/book that discusses symmetry breaking in terms of roots and weights.
Any suggestions would be much appreciated!
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How do fundamental symmetries vanish at the macroscopic level?
I recently read an interesting discussion, between Carlo Rovelli and Steven Weinberg which happened at the "Conceptual Foundations of Quantum Field Theory" conference in 1994:
Rovelli: Steve, you …
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