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38
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2answers
878 views

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 ...
36
votes
10answers
4k views

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 ...
23
votes
1answer
601 views

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 ...
22
votes
1answer
515 views

Finding the vacuum which breaks a symmetry

I will start with an example. Consider a symmetry breaking pattern like $SU(4)\rightarrow Sp(4)$. We know that in $SU(4)$ there is the Standard Model (SM) symmetry $SU(2)_L\times U(1)_Y$ but depending ...
20
votes
2answers
2k views

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 ...
20
votes
1answer
1k views

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 ...
15
votes
2answers
720 views

What is (meant by) a non-compact $U(1)$ Lie group?

In John Preskill's review of monopoles he states Nowadays, we have another way of understanding why electric charge is quantized. Charge is quantized if the electromagnetic U(l)em gauge group ...
15
votes
1answer
530 views

Does the existence of Higgs imply the existence of Magnetic Monopoles?

I am aware that in theories with spontaneous symmetry breaking, Magnetic Monopoles can exist as topological solitons. Can the same be done with the Standard Model gauge group. I am familiar with the ...
15
votes
2answers
2k views

Self energy, 1PI, and tadpoles

I'm having a hard time reconciling the following discrepancy: Recall that in passing to the effective action via a Legendre transformation, we interpret the effective action $\Gamma[\phi_c]$ to be ...
14
votes
1answer
571 views

Spontaneous breaking of Lorentz invariance in gauge theories

I was browsing through the hep-th arXiv and came across this article: Spontaneous Lorentz Violation in Gauge Theories. A. P. Balachandran, S. Vaidya. arXiv:1302.3406 [hep-th]. (Submitted on 14 ...
14
votes
1answer
280 views

Explicit supersymmetry breaking fermion mass terms

I hope you can clear up my following confusions. In Girardello's and Grisaru's paper (Nuclear Physics B, 194, 65 (1982)) where they analysed the most general soft explicit supersymmetry breaking ...
13
votes
3answers
1k views

Why is the Symmetry Group for the Electroweak force $SU(2) \times U(1)$ and not $U(2)$?

Let me first say that I'm a layman who's trying to understand group theory and gauge theory, so excuse me if my question doesn't make sense. Before symmetry breaking, the Electroweak force has 4 ...
12
votes
2answers
360 views

In what sense do Goldstone bosons live in the coset?

Goldstone's theorem says that if a group, $G$, is broken into its subgroup, $H$, then massless particles will appear. The number of massless particles are given by the dimension of the coset, $G/H$. ...
11
votes
2answers
3k views

Spontaneous Time Reversal Symmetry Breaking?

It is known that you can break P spontaneously--- look at any chiral molecule for an example. Spontaneous T breaking is harder for me to visualize. Is there a well known condensed matter system which ...
11
votes
0answers
278 views

“S-duality” between confinement and the Higgs mechanism?

I feel picked by the second to last sentence in this answer to a question about what would happen if EM and QCD were spontaneously broken, which says "In fact, there is a sense in theoretical ...
10
votes
2answers
1k views

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 ...
10
votes
3answers
1k views

How come a photon acts like it has mass in a superconducting field?

I've heard the Higgs mechanism explained as analogous to the reason that a photon acts like it has mass in a superconducting field. However, that's not too helpful if I don't understand the latter. ...
10
votes
2answers
705 views

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 ...
10
votes
1answer
293 views

Chiral perturbation theory: what is the Quark Condensate? why expand in $U$ rather than Goldstone fields?

I'm studying Chiral Perturbation Theory ($\chi PT$) from Scherer's Introduction to Chiral Perturbation Theory. What I am currently having some trouble understanding are two things: The quark ...
10
votes
1answer
123 views

Breaking of E6 to SO(10) in heterotic string theory

Some of the heterotic string models have an $E_6\otimes E_8$ symmetry. Examples include some orbifold models, some free fermionic models and Gepner models. We can break the gauge symmetry by including ...
9
votes
2answers
471 views

Could spontaneous symmetry breaking happen again in our universe?

It is generally believed that $10^{-35}$ seconds after the Big Bang, the symmetry of a GUT was broken and after $10^{-12}$ seconds the electroweak force was broken: \begin{equation} \mathrm{SU(2)} ...
9
votes
2answers
689 views

Understanding Elitzur's theorem from Polyakov's simple argument?

I was reading through the first chapter of Polyakov's book "Gauge-fields and Strings" and couldn't understand a hand-wavy argument he makes to explain why in systems with discrete gauge-symmetry only ...
9
votes
1answer
1k views

Topological order vs. Symmetry breaking: what does (non-)local order parameter mean?

Topological order are sometimes defined in opposition with the order parameter originating from a symmetry breaking. The latter one being possibly described by a Landau theory, with an order ...
9
votes
3answers
1k views

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 ...
9
votes
1answer
959 views

Possibility of Bose-Einstein condensation in low dimensions

I remember having a problem (for practice preliminary exams at UC Berkeley) to prove that Bose-Einstein condensation(BEC) is not possible in two dimensions (as opposed to three dimensions): For ...
9
votes
1answer
225 views

A graphical proof that the $SU(2)/\mathbb{Z}_2$ vortex is non-orientable

The text, see [1], compares the vortex solutions of a spontaneously broken symmetry $U(1) \rightarrow 1$ and $SU(2)\rightarrow U(1) \rightarrow \mathbb{Z}_2$. The vortices can be classified by ...
9
votes
3answers
550 views

Spontaneous breaking of Lorentz invariance

Is it possible to spontaneously break Lorentz invariance, i.e., have a Lagrangian that respects LI but a vacuum which does not? If it is possible, why isn't there even the slightest hint of the ...
9
votes
1answer
351 views

Vibrational anharmonic coupling and noise-induced spontaneous symmetry breaking in a hexagonal finite mechanical lattice

Happy holidays, everyone! The following is part question, part visual gallery, and part classical mechanics problem. Inspired by snow over the weekend I began simulating the vibrations of the ...
8
votes
2answers
2k views

Why do we need Higgs field to re-explain mass, but not charge?

We already had definition of mass based on gravitational interactions since before Higgs. It's similar to charge which is defined based on electromagnetic interactions of particles. Why did Higgs ...
8
votes
2answers
409 views

Precise statement of Mermin–Wagner theorem

Roughly speaking, Mermin-Wagner theorem states that continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions ...
8
votes
2answers
181 views

Can a superpartner be less massive than its SM counterpart?

Theoretically, can a superpartner be less massive than its standard model counterpart? I realize there are experimental constraints.
8
votes
1answer
547 views

Dispersion of ferromagnetic ($E\propto k^2$) and antiferromagnetic ($E\propto k$) spin wave

The dispersion of ferromagnetic spin wave at low energy is $E\propto k^2$, while $E\propto k$ for antiferromagnetic case. Is there a simple/physical argument (such as symmetry) for these results? ...
8
votes
1answer
129 views

Which is the coupling between the photon and the SU(2)xU(1) gauginos, before symmetry breaking?

The photon field is the non chiral piece of SU(2)xU(1), independently of symmetry breaking or not, isn't it? But before symmetry breaking, each gauge boson has only a chiral gaugino as ...
8
votes
2answers
339 views

Do the standard cosmology models spontaneously break Lorentz symmetry?

In standard cosmology models (Friedmann equations which your favorite choice of DM and DE), there exists a frame in which the total momenta of any sufficiently large sphere, centered at any point in ...
8
votes
2answers
543 views

Dynamical supersymmetry breaking and Witten index

Witten index, defined as ${\rm Tr}(-1)^F$, determines if supersymmetry is spontaneously broken or not for a given model. However, it is also known that supersymmetry can be dynamically broken. One ...
8
votes
2answers
382 views

Time crystals : fake or revolution?

This article about "crystals of time" just appeared on the PRL website. Viewpoint: Crystals of Time (http://physics.aps.org/articles/v5/116) The authors (including famous Frank Wilczek) claim that ...
8
votes
2answers
617 views

Symmetry Breaking And Phase transition

Is every phase transition associated with a symmetry breaking? If yes, what is the symmetry that a gaseous phase have but the liquid phase does not? What is the extra symmetry that normal $\bf He$ ...
8
votes
1answer
382 views

What is the difference between quantum fluctuations and thermal fluctuations?

Start with a simple scalar field Lagrangian $\mathcal{L}(\phi)$ at zero temperature $T = 0$, which has a hidden symmetry and spontaneously break it. By the standard procedure a field $\phi$ is ...
8
votes
0answers
130 views

Simple argument for unexpected behavior in SUSY model

Consider a supersymmetric theory with 3 chiral superfields, $X, \Phi_1$ and $\Phi_2,$ with canonical Kahler potential and superpotential $$ W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ ...
7
votes
1answer
288 views

Where does the hidden supersymmetric sector of the MSSM come from?

At the end of Chapter 14 of the "Supersymmetry Demystified book" from Patrick Labelle it is mentioned that to constrain the number of allowed softly SUSY breaking terms, a shadow or hidden ...
7
votes
1answer
509 views

Early time in the Big Bang

I am not a physicist, so I would really appreciate using a simple language for the explanation of my question. From what I understood at the early Big Bang the four fundamental forces were unified to ...
7
votes
1answer
335 views

If a symmetry operator S in a QFT annihilates the vacuum, why does S preserve the space of 1-particle states?

In the paper "Supersymmetry and Morse Theory", on the third page (p. 663 in the journal version), Witten says: "Now in any quantum field theory if a symmetry operator (an operator which commutes ...
7
votes
2answers
229 views

What's the heuristic reasoning for Chiral Symmetry breaking

In Peskin and Schroeder (page 669), and other references, the heuristic reasoning for why one would expect chiral symmetry breaking at low energies is that quark masses are small and hence it's not ...
7
votes
1answer
327 views

Where is the “true” Higgs if the LHC 125 GeV signal is rather a higher dimensional radion than a SM Higgs?

In this article, Lumo introduces and explains the idea (presented by the original authors in this paper) that the LHC signal at about 125 GeV could alternatively be interpreted as a higher ...
7
votes
1answer
231 views

Does measurement, quantum in particular, always increase the total entropy?

Measurement of a quantum observable (in an appropriate, old-fashioned sense) necessarily involves coupling to a system with a macroscopically large number of degrees of freedom. Entanglement with this ...
7
votes
1answer
188 views

Intuitive explanation of how hadron mass emerges from the strong force

I'm not familiar with QCD, but I'm looking for intuitive explanation of this phenomenon (it could be that easy explanation does not exist). What I've read is that large part of hadron masses arises ...
7
votes
0answers
361 views

What is the difference and similarities between Stueckelberg mechanism and Higgs mechanism?

What is the difference and similarities between Stueckelberg mechanism and Higgs mechanism? They both make the gauge field massive. Is the Stueckelberg mechanism a special case about U(1) gauge fields ...
7
votes
3answers
157 views

What role does “spontaneously symmetry breaking” played in the “Higgs Mechanism”?

In talking about Higgs mechanism, the first part is always some introduction to the concept of spontaneously symmetry breaking (SSB), some people saying that Higgs mechanism is the results of SSB of ...
6
votes
1answer
286 views

Could dark matter be a kind of Goldstone boson?

The common argument for vanishing Goldstone boson is like, if there is some massless particle generated from the spontaneous symmetry breaking, it should be detected. Since we never saw that, it is ...
6
votes
2answers
233 views

Coupling constant in electroweak theory

Electroweak theory has two coupling constants before and after Spontaneous Symmetry Breaking (SSB) each one for $SU(2)_L$ and $U(1)_Y$, though they are connected by Weinberg angle after SSB. My ...