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5
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1answer
186 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 ...
6
votes
1answer
110 views

Spontaneous symmetry breaking and time-reversal symmetry

In most textbooks on field theory you read that "spontaneous symmetry breaking implies degeneracy of the ground state". (Like for example in ...
2
votes
1answer
54 views

How do gauginos and scalars gain masses after gauge-mediated symmetry breaking?

In the minimal-GMSB model, the messenger fields transform under the MSSM gauge group and connect a so-called hidden sector to the visible sector. These meesenger fields (left-handed chiral ...
1
vote
1answer
31 views

What is the general conditions for non-zero polarization?

I only know that for a system to have non-zero polarization it should break inversion symmetry. What about others requirements?
2
votes
1answer
49 views

Glashow-Weinberg-Salam mass terms

At the end of spontaneous symmetry breaking I get these mass terms: $$W_{\mu}^{\pm}=\frac{1}{\sqrt{2}}\bigl(W_{\mu}^{1} \mp i W_{\mu}^{2} \bigr )$$ $$\mathcal{L}_{mass}=\frac{1}{2} g^2 \frac{v^2}{4} ...
9
votes
1answer
210 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 ...
8
votes
3answers
679 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 ...
3
votes
0answers
65 views

Why is there a 'loophole' in Mermin Wagner for rotations?

I'm just starting out in my mathematics career by looking at some simple stuff on broken symmetries in statistical mechanics. Since 3D is 'hard' it would be very nice to look at 2D toy models of ...
7
votes
2answers
146 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 ...
3
votes
1answer
89 views

What is physical meaning of $|\phi|^2$ in quantum field theory and pedagogical spontaneous symmetry breaking?

If wavefunction is $\phi$, we know that $|\phi (x)|^2$ represents probability of finding a particle at $x$. Now let us talk about some pedagogical example in spontaneous symmetry breaking in QFT, ...
3
votes
1answer
132 views

Spontaneous Symmetry Breaking

In Spontaneous symmetry breaking we have got that, a field $$\phi= \pm \sqrt{\frac{-m^2}{\lambda}}.$$ Now in order to get the unstable minima we need to guess the mass $m^2 <0 $. But can mass be ...
37
votes
2answers
668 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 ...
3
votes
0answers
38 views

Spontaneous breaking of a discrete non-Abelian symmetry

Can someone give an example of an one dimensional local gapped quantum lattice model with a discrete non-Abelian global internal symmetry that is spontaneously broken in the ground state? In ...
5
votes
2answers
74 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 ...
1
vote
0answers
75 views

Renormalizability of standard model

I'm wonder what precisely is meant by the renormalizability of the standard model. I can imagine two possibilities: The renormalizability of all of the interaction described by the Lagrangian before ...
8
votes
2answers
318 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 ...
5
votes
1answer
112 views

What do we mean when we say Bose condensation? And why can't fermions condense if they don't pair?

In common textbooks, we are told that bosons can condense in a single-particle state because of bose statistics and when the system undergoes a bose condensation, the bose field operator obtains a ...
14
votes
1answer
212 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 ...
3
votes
1answer
171 views

Definition for Chiral Spin Liquid

What is the definition of chiral spin liquid? Especially what does chiral mean here? I encounter a lot of terminologies with chiral. It seems they mean differently in different contexts. If you could ...
10
votes
2answers
202 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, $G/H$. ...
3
votes
1answer
68 views

Symmetry breaking of the hidden sector

Lately, I have some read some papers about the hidden sector of particle physics which combines with the Standard Model through the so-called Higgs portal. Let the Lagrangian for this be composed of ...
2
votes
0answers
30 views

How does the choice of a particular vacuum in a field theory problem decide the number of Goldstone bosons?

How does the field expansion method (by this I mean expanding your fields about a chosen VEV and plugging into a given potential so that the masses of the fields are given by the coefficients in ...
1
vote
0answers
16 views

How does the choice of a basis decide how many Goldstone bosons there are under spontaneous symmetry breaking?

I have a question about how the basis you choose in a field theory problem semmingly decides how many Goldstone bosons you get after spontaneous symmetry breaking. For SU(2), if you choose the 3 Pauli ...
4
votes
1answer
62 views

Number of Goldstone bosons in paramagnetic-to-ferromagnetic phase transitions

In paramagnetic-to-ferromagnetic phase transitions, the symmetry spontaneously breaks down from SO(3) to the subgroup SO(2) below $T_\text{crit}$. This implies that there should be two Goldstone modes ...
5
votes
2answers
255 views

Naive questions on Goldstone modes and a possible duality relation?

For example, let's consider a 1D spin-1/2 ferromagnetic (FM) Heisenberg chain $H=-J\sum_{i=1}^{N}\mathbf{S}_i\cdot\mathbf{S}_{i+1}$ with periodic boundary conditions. Now we want to study its low ...
15
votes
0answers
240 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 ...
3
votes
1answer
76 views

How does one prove that the current of a spontaneously broken symmetry generates a particle?

I am having a hard time arguing that, after spontaneous breaking of a continuous symmetry of a field Lagrangian, local fluctuations around the vacuum can be interpreted as particles (without referring ...
1
vote
0answers
46 views

What is the minimal symmetry required for a spin Hamiltonian to describe a spin-liquid ground state?

Let's restrict to the case of spin-1/2 system. As we know, a spin-liquid (SL) state is the ground state of a lattice spin Hamiltonian with no spontaneous broken symmetries (sometime it may ...
3
votes
2answers
239 views

Domain walls intersection

I was reading this article(On domain shapes and processes in supersymmetric theories). In the paragraph about domain walls intersection (paragraph $4$, page $7$) the authors say: In a one-field ...
2
votes
1answer
45 views

Why does the symmetry breaking parameter `$v$' have dimensions of mass

A symmetry is spontaneously broken by an operator $\hat{O}$ which acquires a non-zero vacuum expectation value. This is expressed as $$ \langle 0 | \hat{O} | 0 \rangle = v$$ The parameter $v$ is ...
3
votes
1answer
155 views

Why are there gapless excitations in the anti-ferromagnetic Heisenberg model while the true ground state is a singlet?

The true ground state of the anti ferromagnetic quantum Heisenberg Model (nearest neighbor only)is known to be a singlet (I think this is Liebs theorem.) Since a singlet is invariant under rotations, ...
6
votes
1answer
235 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 ...
9
votes
2answers
309 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
176 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 ...
15
votes
2answers
1k 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 ...
15
votes
1answer
460 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 ...
5
votes
0answers
54 views

Is there a soft Goldstino theorem?

For ordinary spontaneously broken symmetries, you can demonstrate relations between S-matrix elements with a soft goldstone emission and another S-matrix element without the emission. If I break ...
9
votes
2answers
360 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)} ...
0
votes
0answers
98 views

Examples of symmetric field collapse to produce asymmetry

It would really help me with an idea I have if I could see how something such as a symmetric field could collapse to something asymmetric. I know that if $x$ occures before $y$ is symmetric, then $y$ ...
2
votes
1answer
100 views

How do photons decay in superconductors?

If $A$ is the vector potential, the London equations imply that: $$(\nabla^{2}-\mu^{2})A=0$$ if there is no external current. This can be interpreted as an effective photon mass and so, light ...
2
votes
1answer
82 views

Goldstone boson couple to conserved current

The Goldstone boson in spontaneous symmetry breaking problem couples naturally to the associated conserved current of the broken symmetry. How can I see a rigorous (mathematical) derivation for that?
6
votes
2answers
211 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
3answers
583 views

Why is the Symmetry Group for the Electroweak force SU(2)xU(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 ...
0
votes
1answer
83 views

Amplitudes involving Goldstone bosons

Does anyone know some theorem or statement about amplitudes involving only Goldstone bosons in theories with spontaneous symmetry breaking in the limit of low energies?
5
votes
1answer
98 views

Quantum Anomalies for Bosons

We know that there is Adler and Bell-Jackiw(ABJ) type anomalies for fermions. In some case, the ABJ anomaly affecs particle physics pheonomelogy, such as pion decays or kaon decays(in the case of ...
1
vote
1answer
98 views

The self-coupling constant for the Higgs mechanism

I have a few questions about the parameter $\lambda$ in the Higgs-Lagrangian density $$\mathcal{L}_H=(D_\mu \phi)^\dagger D_\mu \phi + \mu^2\phi^\dagger\phi-\lambda(\phi^\dagger\phi)^2$$ Is it ...
3
votes
0answers
35 views

Detecting Polarization States of Quantum Field

(Background) In the scenario where a gauge symmetry is spontaneously broken and the gauge field eats the Goldstone boson to acquire a mass, the massive gauge field acquires a longitudinal ...
3
votes
0answers
75 views

A question about spontaneous symmetry breaking at macroscopic limit

The question relates to this post. Spontaneous symmetry breaking is somehow a volume effect, that in-principle only happens at infinity large system. Weinberg in the second volume of his QFT used a ...
5
votes
1answer
183 views

Why must SUSY be broken?

Background One usually claims that supersymmetry must be spontaneously broken. The reasoning is roughly the following: Since $M^2=P^{\mu}P_{\mu}$ is a casimir operator of the supersymmetry algebra, ...
7
votes
0answers
108 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 $$ W= \frac12 h_1 X\Phi_1^2 +\frac12 h_2 \Phi_2\Phi_1^2 + fX.$$ ...