Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [symmetry-breaking]

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.

1
vote
1answer
76 views

Misconceptions in spontaneous symmetry breaking

Spontaneous symmetry breaking occurs when we have a potential like a mexican hat as shown in figure (right) and is unbroken for the potential shape as shown in left figure. Under the Symmetry ...
2
votes
1answer
32 views

Polar representation of complex scalar field in spontaneous symmetry breaking

In Rubakov's "Classical Theory of Gauge Fields", in the chapter on Higgs mechanism, he mentions that you can switch to the polar form of the complex scalar field only for non-zero vacuum value of the ...
2
votes
0answers
35 views

Shift symmetric scalar field

Suppose I study a quantum field theory in which among other fields a shift symmetric scalar field appear: $$\phi\rightarrow\phi+c$$ with $c$ a real constant. Can this always be interpreted as a Nambu-...
9
votes
2answers
186 views

Spontaneous symmetry breaking: proving the equivalence of two definitions

This question can be posed for both quantum and classical set-ups. For concreteness, let me consider a local, classical Hamiltonian $H$. The expectation values I consider are with respect to the usual ...
0
votes
0answers
24 views

Spinwaves, Mermin-Wagner theorem, Two-point correlation function and Heisenberg model

I was looking at the Mermin-Wagner theorem (as following the previous question) and the Heisenberg model seems to be presented, and they split the Hamiltonian $H$ in the matrix or vector n-components ...
0
votes
0answers
21 views

What happens to the (Wilsonian) effective action if a symmetry is spontaneously broken?

A spontaneously broken symmetry is a symmetry of the action which does not manifest itself in physical states. Since the action is still invariant under this symmetry, can we say the same about the ...
3
votes
1answer
181 views
+100

Relating the Yang-Mills field-strength to the Maxwell tensor in $SU(2)$ gauge theory

I'm studying topological monopoles in a $SU(2)$ Yang-Mills theory with spontaneous symmetry breaking, through the book "Topological Solitons", by Manton and Sutcliffe. In section 8.2, the authors ...
7
votes
1answer
98 views

Mermin-Wagner and graphene

I have been told that the Mermin-Wagner theorem disallows the existence of the crystal of graphene. However, I don't have enough knowledge to understand the Mermin-Wagner theorem. If possible can ...
5
votes
1answer
77 views

Detecting the electroweak unification in data of quark gluon plasma

Electroweak unification is discussed in the Big Bang model and variant proposals, and there is a transition at energies of 100 GeV where the EW symmetry is unbroken and a quark gluon plasma phase ...
1
vote
1answer
27 views

Super GoldStone model and SuperHiggs theorem

I am currently studying SuperSymmetry and I have reached a problem which I have not found an answer to. I clearly understand how the Goldstone theorem works for the boson case (without any susy) ...
4
votes
0answers
60 views

If the gauge symmetry is not broken by spontaneous symmetry breaking, what symmetry is broken?

In this post, the answer by buzhidao showed that the $U(1)$ gauge symmetry is not broken by spontanous symmetry broken and Higgs mechanism. What role does "spontaneously symmetry breaking" ...
1
vote
2answers
111 views

Goldstone bosons when SSB potential has two fields

A theory consists of two complex scalar fields $φ_0$ and $φ _1$ with a symmetry-breaking potential $$V(|φ_0|^2 + |φ_1|^2).$$ How many Goldstone particles will there be in the theory?
1
vote
0answers
18 views

Mass splitting for leptons and down quarks in $SU(5)$ model?

In the minimal $SU(5)$ GUT model, the masses of the leptons and the corresponding down-type quarks must be equal. i.e. $m_e=m_d$, $m_\mu=m_s$, $m_\tau=m_b$. Whereas this is approximately correct for ...
1
vote
0answers
10 views

Axion CDM analogous to reheating?

In a paper on Axions Peccei writes: When the Universe goes through the PQ phase transition at $T ∼ f_a > > Λ_{QCD}$ the QCD anomaly is ineffective. As a result, early in the Universe $< ...
0
votes
0answers
16 views

Direction of chiral symmetry breaking

What happens if one breaks the SU(2) chiral symmetry in a non-real direction(a direction apart from the one that the small masses of hadron's constituents(quarks) dictate). Or equivalently We know ...
1
vote
0answers
20 views

Could electroweak interactions derive from higgsing of gauged chiral symmetry?

A recent question discussed the practice of introducing electroweak interactions into chiral perturbation theory by gauging part of the chiral symmetry. Gauging chiral symmetry is normally regarded as ...
1
vote
3answers
131 views

Embedding of $SU(2)_L \times U(1)_Y$ into $SU(2)_L \times SU(2)_R$ in electroweak chiral effective theories

In the context of chiral effective theories we usually deal with the pion field \begin{equation} U= ie^{\frac{\pi^a \sigma^a}{2f}} \end{equation} where $\pi^a=\big(\pi^1, \pi^2, \pi^3\big)$ are the ...
7
votes
1answer
167 views

Is Lorentz symmetry broken if SUSY is broken?

I have seemingly convinced myself that the entire Poincare group is spontaneously broken if one of the supersymmetric charges is spontaneously broken. We know that if one of the supersymmetric ...
0
votes
0answers
8 views

Kitaev's reason for looking at p-wave superconductors

I would really like to understand the thought process that lead Kitaev to proposing the Kitaev chain but most expositions really just start from the Hamiltonian and derive the Majoranas without any ...
2
votes
0answers
20 views

How to break softly a symmetry

If you start from a theory (non-SUSY) with whatever symmetry and you break it by adding a soft term. Do you have to add to your Lagrangian all possible soft terms that break the symmetry? If so, why? ...
1
vote
1answer
142 views

Simplest model in field theory which leads to a pseudo-Goldstone boson

What can be a simple (if not simplest) continuum field theory model that gives rise to a pseudo Goldstone boson (doesn't matter if it is a toy model)? For example, I would be very happy if one can ...
0
votes
1answer
73 views

Symmetry and symmetric vacuum in Quantum Field theory

In the start of section 28.2 of Schwartz's Quantum Field theory and the Standard Model, Schwartz states that for a conserved charge, $\hat{Q}$, which generates the corresponding symmetry ...
2
votes
3answers
186 views

Why a field theory containing only fermions does not show spontaneous symmetry breaking?

For a real scalar field $\phi$, a theory as simple as the $\phi^4$ theory, can exhibit the phenomenon of Spontaneous Symmetry Breaking (SSB). For a complex scalar field $\phi$, a theory as simple as ...
1
vote
1answer
51 views

Why is the approximate $\rm U(2)\times U(2)$ global symmetry of QCD that has a special importance?

I was looking at Peskin and Schroeder (Section 19.3, page $667-668$). They talk about $\rm U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this ...
0
votes
1answer
57 views

Why isn't superconductivity destroyed by the Goldstone modes?

In BCS theory they break particle number conservation and show the existence of a gap, which would explain why groundstate properties stay relatively the same even for higher temperatures (until beta ...
2
votes
1answer
78 views

A couple of questions about spontaneous symmetry breaking (SSB)

I have a few doubts about my understanding of spontaneous symmetry breaking. To keep it simple, I will take a global U(1) transformation on a complex scalar field as an example. The questions are ...
0
votes
0answers
58 views

Unitary gauge for spontaneous symmetry breaking

I'm given a lagrangian $$ \mathcal{L} = \partial_{\mu} \Phi^{\dagger} \partial^{\mu} \Phi + m^2 \Phi^{\dagger} \Phi - \lambda (\Phi^{\dagger} \Phi)^2 $$ where $m^2 > 0, \lambda > 0$. This ...
0
votes
0answers
9 views

Physical interpretation of Bogolyubov sound with zero momentum in BEC

The point with zero momentum in the spectrum of acoustic phonon corresponds to a translation of the crystal. Is there an interpretation like this of the Bogolyubov sound in BEC? I have read that in ...
3
votes
0answers
43 views

Collective modes of charge density wave

The question is about collective modes of charge density waves, i.e., amplitude and phase fluctuations $\delta,\phi$ of the order parameter $\Delta(x,t)=(\Delta_0+\delta)e^{i\phi}$. I read on p.1 of ...
2
votes
2answers
76 views

How can I simulate a ground state degenerate system numerically?

I'm using numerical method like DMRG to simulate ground state of correlated systems. But the degeneracy of the ground state has long bothered me: When degeneracy exists the ground state isn't unique. ...
1
vote
0answers
50 views

What is the standard definition of quantum spontaneous symmetry breaking?

i found many answers about spontaneous symmetry breaking here but i am not sure to see what is the standard definition of SSB. i am interested in the BCS theory and i would like to know how the ...
1
vote
1answer
83 views

$W$, $Z$ bozons and fermions gained their masses WHEN?

I have read these questions: How does the Higgs mechanism work? How does the Higgs boson give mass to other elementary particles like electrons? What is the difference between the Higgs Boson ...
3
votes
0answers
82 views

What is the 't Hooft determinant?

The 't Hooft vertex/determinant is somehow generated by instantons and is responsible for the generation of mass gap in pseudo-Goldstone bosons, such as an axion. For example, the complex Peccei-...
1
vote
0answers
54 views

How do we determine who eats who (or which field gets massive) in a Higgs phase transition?

Consider the following theory in which a $2$-form field $B_{\mu\nu}$ with field strength $P_{\alpha\mu\nu}=\partial_{[\alpha}B_{\mu\nu]}$ is coupled to a $3$-form gauge field $C_{\alpha\beta\gamma}$ ...
0
votes
0answers
21 views

Why do we have constraints on the baryon asymmetry of the universe and not the lepton asymmetry?

What is it about baryons that means that CMB observations can determine their asymmetry without also including a charged leptonic component?
0
votes
0answers
40 views

Where is the gauge symmetry in an ideal Bose gas?

It seems in the literature that there is a certain notion of a “macroscopic wavefunction” associated with a Bose-Einstein system (see this PSE answer) which exhibits a global $U(1)$-phase symmetry. ...
0
votes
2answers
85 views

Understanding Ising Model in Statistical Mechanics

A section on the Ising model in the text "Introduction to modern statistical mechanics" by Chandler states the following: "We consider a system of $N$ spins arranged on a lattice. In the ...
0
votes
1answer
85 views

Obtaining an expression for spontaneous magnetization in 1D Ising model with $H=0$ from the beginning

The usual trick to find the spontaneous magnetization for the 1D Ising model is to calculate the partition function $Z$ with the Hamiltonian $$\mathscr{H}=-J\sum\limits_{i}S_iS_{i+1}-H\sum\limits_{i}...
0
votes
1answer
70 views

Order parameter and Bose-Einstein condensation

I want to study about order parameter and symmetry breaking related to bose einstein condensation in interacted system. Which book i should read? also i want to learn this in second quantization ...
2
votes
1answer
33 views

What happens to the massive gauge bosons in a simple Little Higgs model?

I'm trying to understand a simple Little Higgs (toy) model where the Higgs doublet is made of pseudo Nambu-Goldstone Bosons generated by breaking the symmetry from $SU(3)_L\times U(1)_Y$ to $SU(2)_L\...
1
vote
2answers
106 views

Mermin Wagner theorem proof, what does the K stand for ?

I've been reading about the Mermin-Wagner theorem recently. I think I understand pretty much every computation need to derive its result from the Bogoliub inequality, but there is one thing I don't ...
1
vote
1answer
93 views

Goldstone theorem in Weinberg vol 2

I was reading the proof of Goldstone's theorem (the operator proof starting on page 170) in Weinberg's book on QFT (Volume II) and got confused. I am able to follow each line of the proof, but as a ...
3
votes
2answers
77 views

Leptons during Electroweak Epoch

Prior to the electroweak force splitting, did charged leptons still carry a charge of $e$? I was under the impression that, since electromagnetism didn't exist in its current state prior to ...
2
votes
1answer
163 views

Why did David Tong say that the global topological $U(1)$ symmetry is unbroken in Higgs phase?

In the paper A Duality Web in 2+1 Dimensions and Condensed Matter Physics by Seiberg, Senthil, Wang, and Witten, they studied the particle-vortex dualities in $2+1$ dimensions. On page 20, section 3....
7
votes
1answer
156 views

Anomaly is due to the noninvariance of the path-integral under a symmetry. Is the noninvariance reflected on 1PI effective action?

When a symmetry is anomalous, the path integral $Z=\int\mathcal{D}\phi e^{iS[\phi]}$ is not invariant under that group of symmetry transformations $G$. This is because though the classical action $S[\...
3
votes
2answers
86 views

How do know that Goldstone Boson actually become the longitude degrees of freedom in W+,W- and Z boson?

In many Quantum Field Theory text books they says these about Spontaneous Breaking and Higgs mechanism like this In unitary gauge, the Goldstone Bosons are eaten by $W^\pm$ and Z and become their ...
7
votes
1answer
86 views

Does a symmetry operator $U$ and its generator $Q$ acting on a vacuum $|0\rangle$ both represent new degenerate vacuum?

After the spontaneous breakdown of a symmetry characterized by $$\hat{U}=e^{i\hat{Q}\theta},$$ the commutation relation $[H,Q]=0$ continues to hold. Let us consider two states after this symmetry ...
1
vote
0answers
32 views

Symmetry breaking with Kinetic term dominating the Potential on a Lagrangian

Suppose a Lagrangian $L$ for a scalar field $\phi$, consists of a kinetic term and a Mexican-hat type potential. I am aware that if the vacuum has symmetry $H \subset G$ while the Lagrangian has ...
0
votes
1answer
98 views

Symmetry-breaking matrix/operator deformations: uniquely splitting eigenspaces into smaller ones?

Operators used in quantum mechanics, like Hamiltonian or angular momentum operator, usually have huge degeneracy of eigenspaces (symmetry inside them) - bringing a question of possibility to uniquely ...
7
votes
6answers
3k views

Can any body be uniform in the universe?

If I take any body in the shape of a rod and stretch that, after it reaches breaking stress it breaks at one point. Even though we apply the same the stress on each and every part of the rod it broke ...