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.
Questions tagged [symmetry-breaking]
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What is spontaneous symmetry breaking in quantum systems?
Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture.
According to the classical picture, spontaneous symmetry breaking can only happen for non-linear…
Xiao-Gang Wen
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First and second order phase transitions
Recently I've been puzzling over the definitions of first and second order phase transitions. The Wikipedia article starts by explaining that Ehrenfest's original definition was that a first-order transition exhibits a discontinuity in the first…
N. Virgo
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Norton's dome and its equation
Norton's dome is the curve $$h(r) = \frac{2}{3g} r ^{3/2}.$$ Where $h$ is the height and $r$ is radial arc distance along the dome. The top of the dome is at $h = 0$.
Via Norton's web.
If we put a point mass on top of the dome and let it slide down…
countunique
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Symmetries of the Standard Model: exact, anomalous, spontaneously broken
There are a number of possible symmetries in fundamental physics, such as:
Lorentz invariance (or actually, Poincaré invariance, which can itself be broken down into translation invariance and Lorentz invariance proper),
conformal invariance (i.e.,…
Gro-Tsen
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Do pear-shaped nuclei really have anything to do with time travel?
Recently (in the last week or two), various articles about pear shaped nuclei have appeared, such as this one from Science Alert and this from the BBC
The Science Alert article includes the quote
We've found these nuclei literally point towards a…
Matt
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What role does "spontaneous symmetry breaking" play in the "Higgs Mechanism"?
In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneous symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of local gauge symmetry, some people says that we can…
an offer can't refuse
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How does the Higgs mechanism work?
I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost.
Is there a way to explain how the Higgs field works, in a way that people like me might have a hope of understanding?
Mike Dunlavey
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Emergent symmetries
As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ground state breaks the symmetry.
But what about…
Kai Li
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What is (meant by) a non-compact $U(1)$ Lie group?
In John Preskill's review of monopoles he states on p. 471
Nowadays, we have another way of understanding why electric charge is quantized. Charge is quantized if the electromagnetic $U(l)_{\rm em}$ gauge group is compact. But $U(l)_{\rm em}$ is…
twistor59
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Understanding time crystals
In very recent publications, two groups in Maryland (paper: "Observation of a Discrete Time Crystal") and Harvard (paper: "Observation of discrete time-crystalline order in a disordered dipolar many-body system") have separately worked on…
user929304
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How does the Super-Kamiokande experiment falsify SU(5)?
In his book "The Trouble With Physics", Lee Smolin writes that he is still stunned by the falsification of the $SU(5)$ Georgi-Glashow model by the null results of proton decay experiments.
I should like a simple but, if possible, quantitative…
Selene Routley
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Spontaneous symmetry breaking in classical mechanics, quantum mechanics and quantum field theory
I wondered if someone could help me understand spontaneous symmetry breaking (SSB) in classical mechanics, quantum mechanics and quantum field theory. Consider a Higgs-like potential, with a local maximum surrounded by a degenerate ground state - a…
innisfree
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What is the role of the vacuum expectation value in symmetry breaking and the generation of mass?
Consider a theory of one complex scalar field with the following Lagrangian.
$$
\mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\mu ^2\phi ^*\phi -\frac{\lambda}{2}(\phi ^*\phi )^2.
$$
The potential is
$$
V(\phi )=-\mu ^2|\phi …
Jonathan Gleason
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Are there massless bosons at scales above electroweak scale?
Spontaneous electroweak symmetry breaking (i.e. $SU(2)\times U(1)\to U(1)_{em}$ ) is at scale about 100 Gev. So, for Higgs mechanism, gauge bosons $Z$ & $W$ have masses about 100 GeV. But before this spontaneous symmetry breaking ( i.e. Energy > 100…
Eleuname
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For lattice, what are the Goldstone bosons for the broken rotation symmetries?
In $1$ dimension, we know that lattice breaks continuous translational symmetry into discrete translational symmetry, which generates $1$ Goldstone boson, i.e. $1$ longitudinal phonons.
In $d$ dimensions, if there are only $1$ type of atoms, then…
346699
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