Stack Exchange Network

Stack Exchange network consists of 174 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.

0
votes
1answer
49 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
38 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 ...
1
vote
0answers
21 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
58 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
67 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
68 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
0answers
59 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
133 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
62 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 ...
6
votes
1answer
75 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
26 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
89 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 ...
0
votes
1answer
107 views

Doesn't the “Mexican hat” potential give a misleading impression that the barrier height between two vacua is finite?

For $\mathbb{Z}_2$ symmetry breaking in a Classical Field Theory described by a potential $$V(\phi)=\lambda(\phi^2-v^2)^2,\tag{1}$$ there is a finite energy barrier of height $\epsilon=\lambda v^4$ ...
2
votes
1answer
97 views

How is it possible to take the inner product of states which belong to two different Hilbert spaces?

Question 1 In case of spontaneous breakdown of a continuous symmetry e.g. the ${\rm U(1)}$ symmetry, two different vacua can be labelled as $|\theta\rangle$ and $|\theta^\prime\rangle$, and they ...
0
votes
1answer
133 views

Physically, what is the Fabri-Picasso theorem really trying to say?

The Fabri-Picasso (FP) theorem states that if a symmetry is spontaneously broken the corresponding conserved charge operator $Q$ does not exist in the Hilbert space. The state $Q|0\rangle$ will have ...
1
vote
2answers
40 views

Fabri-Picasso theorem: Why can we assume that the charge commutes with momentum?

To prove the Fabri-Picasso theorem, we assume that the charge $Q$ is translationally invariant, i.e. it commutes with the momentum operator: $$ [Q,P^\mu]=0 $$ Why can we assume this?
-1
votes
0answers
49 views

Broken symmetry Ising model

Consider an Ising model for a 2D square lattice where we have interactions for, let's say nearest neighbours and second nearest neighbours $$\mathcal{H}=-J_1\sum_{\langle ij\rangle}\sigma_i\sigma_j-...
3
votes
1answer
76 views

Spontaneous symmetry breaking in fluids

BACKGROUND: One can think of solids as spontaneously breaking translational symmetries in the sense that each atom in a lattice has to pick a particular position. Yet, as with everything in our ...
7
votes
1answer
115 views

Counting degrees of freedom in the Higgs mechanism for different gauges

I am wondering how to count the degrees of freedom (dof) for a massive gauge field in different gauges. I've been reading some other answers, but haven't found a solution yet. I am looking at the ...
6
votes
1answer
120 views

Recovering nonrelativistic quantum mechanics from quantum field theory

In quantum field theory -- specially when applied to high energy physics -- we see that the requirements of Lorentz invariance, gauge invariance, and renormalizability strongly limit the kinds of ...
3
votes
1answer
113 views

How many connected components are there in the vacuum manifold of $\phi^4$ theory?

Consider the following theory in $1+1$ dimensions $$\mathcal L = \frac12(\partial\phi)^2 - \frac\lambda4 (\phi^2 - v^2)^2 \,,$$ which exhibits a $\mathbb Z_2 = \{0,1\}$ symmetry, $\phi \to -\phi$, ...
1
vote
1answer
42 views

Reference request for symmetry breaking Hartree-Fock

Stationary mean-field solutions break symmetries of the many-body Hamiltonian in favour of lowering the energy, e.g. translational or rotational symmetry, despite $[H,P]=0$, or $[H,L_z]=0$, ...
1
vote
1answer
46 views

Group structure of QCD‘s chiral symmetry (breaking)

With $3$ flavors of massless quarks, the QCD Lagrangian is invariant under flavor transformations$$SU(3)_V\ \otimes\ SU(3)_A\ \otimes\ U(1)_V\ \otimes\ U(1)_A.$$ Now, this is equivalent to $$SU(3)_R\ \...
3
votes
2answers
205 views

What is dynamical symmetry breaking, exactly?

As far as I understand, a symmetry can be broken explicitly (either by manually putting symmetry-violating terms in the Lagrangian or via an anomaly) or spontaneously. I want to focus on the second ...
0
votes
0answers
41 views

Matter Anti-matter Imbalance

If both matter and antimatter could still 'pouring out', why do we assume that there is an overall Matter Anti-matter Imbalance? Could not antimatter possibly come out during a different time as ...
0
votes
1answer
32 views

Rest frame of massive photon in Meissner–Ochsenfeld effect

The Meissner–Ochsenfeld effect together with spontaneous symmetry breaking and the London Equation yields $(\Box+M^2)A^\mu=0$ and gives photon an effective mass $q\sqrt{\frac{n_c}{m_c}}$ Which is ...
1
vote
1answer
30 views

Two-nucleon coupling: symmetrization postulate

I have some trouble understanding isospin symmetry. If we consider a system of a proton and a neutron as two different iso-states of a nucleon and we wish to write the wave function, do we have to ...
6
votes
1answer
111 views

Phase Transitions from a Bayesian Perspective of Statistical Mechanics

I have been reading papers by E.T. Jaynes recently about viewing all of statistical mechanics as just Bayesian inference applied to physics. (For an introduction: https://journals.aps.org/pr/abstract/...
0
votes
0answers
56 views

How do right handed quark doublets transform under $SU(2)_R$ transforms?

In the context of proving that the SM custodial symmetry is broken by Yukawa coupling to fermions using a 4D Higgs vector representation, $$\underline{\Phi}=\begin{pmatrix}\Phi\\i\sigma_2\Phi\end{...
1
vote
0answers
41 views

Classification of $E_6$ symmetry breaking

Is there a good reference which details the various ways of breaking $E_6$ into smaller groups using Wilson lines? I'm looking for a list of discrete (Abelian) symmetries, e.g. $\mathbb{Z}_5$, and the ...
4
votes
4answers
111 views

CERN and electroweak interaction

I know that the EM and the weak force were described in the same mathematical formalization by GSW and that it was predicted that they would appear as one at energies of 200 GeV. I know that the $W^+$,...
0
votes
0answers
20 views

Suppressed emission of composite particles

If a composite (pseudo)Goldstone boson $\phi$ emerges in a spontaneous symmetry breaking (similar to the mesons of QCD), is the emission of the $\phi$ particle suppressed in high-energy processes, i.e....
2
votes
1answer
61 views

Parametrization of scalar multiplet for spontaneous symmetry breaking in the non-abelian case

Describing abelian symmetry breaking in his book on gauge theories, after favouring a vacuum (whose expectation value is $v$) from the symmetric continuum, Quigg parametrize the complex scalar as $$ ...
2
votes
0answers
51 views

Elitzur theorem and the Ising model

I was recently studying the Elitzur theorem and its application to the Ising model on Kogut: An introduction to lattice gauge theories and spin systems, chapter $5$C. I was wondering how he obtain $\...
2
votes
1answer
113 views

What does soft symmetry breaking physically mean?

A symmetry can be explicitly broken by adding terms in the Lagrangian that aren't compatible with the symmetry, and we say the symmetry is softly broken if all these terms have positive mass dimension....
6
votes
1answer
377 views

Is spontaneous symmetry breaking robust against weak perturbations to the Hamiltonian?

Setup Suppose we have some Hamiltonian $H$ which is known to exhibit spontaneous symmetry breaking (SSB), at least in some parameter regime. For simplicity, we might consider the 2D Ising model below ...
0
votes
1answer
38 views

Non-abelian Goldstone bosons

Suppose we have a theory with a non-abelian symmetry group $G$ that is spontaneously broken to the subgroup $H\subset G$--this is a global symmetry, $not$ a gauge redundancy. Let $X^a$ be the ...
3
votes
0answers
43 views

Metallic state in 2D

Mermin Wagner theorem prevents any spontaneous breaking of continuous symmetry for short ranged interactions for dimensions, D $\leq$2 for any finite temperature. So I understand that superconducting ...
12
votes
2answers
203 views

If spontaneous symmetry breaking only occurs in infinite systems, why do we observe similar effects in finite systems?

Background No SSB in finite systems Consider a system interacting with a heat bath at inverse temperature $\beta$, with the resultant dynamics of the system described by a Liouvillian superoperator $...
3
votes
1answer
96 views

Symmetry breaking of $SO(10)$ or $Spin(10)$

The Spin(10) grand unification has a symmetry breaking of SO(10), or Spin(10). In Wikipedia, it says, "The symmetry breaking of SO(10) is usually done with a combination of (( a $45_H$ OR a $54_H$...
1
vote
2answers
83 views

Derivation of Casher-Banks relation

Consider two-point function $\langle \bar{\psi}\psi\rangle$ in a model with massive fermions $\psi$ and gauge field: $$ \langle \bar{\psi}\psi\rangle =\frac{1}{V}\sum_{n} \frac{1}{\lambda_{n} +im}, $$...
4
votes
1answer
192 views

Schwartz's and Zee's proof of Goldstone theorem

In Refs. 1 & 2 the Goldstone theorem is proven with a rather short proof which I paraphrase as follows. Proof: Let $Q$ be a generator of the symmetry. Then $[H, Q] = 0$ and we want to consider ...
2
votes
2answers
229 views

Why doesn't Coleman-Mermin-Wanger theorem contradict phase transitions in systems with 1D reaction coordinate?

How does both hold: Coleman-Mermin-Wanger theorem continuous symmetries cannot be spontaneously broken at finite temperature in systems with sufficiently short-range interactions in dimensions ...
1
vote
2answers
90 views

What is spontaneous in spontaneous symmetry breaking

When we say spontaneous symmetry breaking what do we mean by "spontaneous"? The dictionary, for a non native speaker, relates it to the absence of an external stimulus. In QFT and SM it simply says ...
0
votes
0answers
84 views

Dynamics in Higgs mechanism

In "everyday" particle physics, we assume the $ SU(2)_L \times U(1)_Y $ is spontaneously broken to $ U(1)_{EM} $. But in high enough energies the symmetry is restored, otherwise as far as I understand ...
8
votes
1answer
224 views

Breaking a gauge group through a monopole$.$

I am trying to understand the paper arXiv:1712.08639 and, in particular, the discussion in §5. In this section, the authors take a gauge theory with group $\mathrm{SO}(N)$, and they add a "unit of ...
4
votes
2answers
147 views

Why does the covariant derivative not affect the vacuum expectation value of the Higgs field?

Consider the following Lagrangian density: $$ \mathcal{L}_{1} = (\partial_{\mu}\phi^{*})(\partial^{\mu}\phi)-m^{2}\phi^{*}\phi-h(\phi^{*}\phi)^{2} $$ for the complex scalar field $\phi$ with $h>0$. ...
2
votes
1answer
82 views

Simple explanation of the QCD VEV in terms of instantons

I've heard that instantons in QCD generate quark bilinear condensate $\langle \bar{q}_{L}q_{R}\rangle$ which is responsible for spontaneous symmetry breaking. Is there any clear and simple way to ...
0
votes
2answers
121 views

How can spontaneous $P$ or $CP$ violation arise? Examples needed

In quantum field theory, there can be a spontaneous breakdown of discrete and continuous symmetries. Can there be a spontaneous breakdown of P and CP violation where P represents parity and C ...