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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 ...

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Is Higgs mechanism generate mass parameter? Or physical mass?

Is Higgs mechanism generate mass parameter in the Lagrangian? Or physical mass that we can observe in experiment? It is obscure for me how Higgs mechanism produce mass for elementary particle. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $\epsilon=\lambda v^4$ ...
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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 ...
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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 ...
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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?
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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-...
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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 ...
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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 ...
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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 ...
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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, $\phi \to -\phi$, ...
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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 $[H,L_z]=0$, ...
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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\ \...
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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 ...
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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 ...
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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 ...
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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 ...
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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/...
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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{...
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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 ...
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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 $W^+$,...
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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....
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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 $$ ...
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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 $\...
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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....
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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 ...
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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 ...
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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 ...
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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 $...
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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 $54_H$...
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Derivation of Casher-Banks relation

Consider two-point function $\langle \bar{\psi}\psi\rangle$ in a model with massive fermions $\psi$ and gauge field: $$ \langle \bar{\psi}\psi\rangle =\frac{1}{V}\sum_{n} \frac{1}{\lambda_{n} +im}, $$...
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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 ...
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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 ...
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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 ...
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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} $. But in high enough energies the symmetry is restored, otherwise as far as I understand ...
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Breaking a gauge group through a monopole$.$

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 ...
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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 $h>0$. ...
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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 ...
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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 ...
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Does topological mass imply preservation of global symmetry whose current is topological?

This question is general but the motivation for it lies within the paper "A Duality Web in 2+1 Dimensions and Condensed Matter Physics". On pages 20-23, they consider a system which has four phases ...
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Gauge symmetry and symmetry breaking?

In quantum field theory we say that gauge symmetry is a redundancy, and also, in Xiao-Gang Wen's book, it reads that gauge symmetry is not a symmetry, so it can never be broken. And the Higgs ...
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Symmetry breaking - mixed state in $T\rightarrow 0$ limit

In the quantum$^1$ system with a continuous symmetry (in the Thermodynamic limit) relating the ground states $\newcommand{\ket}[1]{\left|#1\right>}\{\ket{\theta}\} \newcommand{\bra}[1]{\left<#1\...
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Are there cross sections with an energy threshold? ($\sigma\sim \Theta(E-E_0)$ )

Is it in principle possible to have a cross section $\sigma$ of a process, say $a \bar{a}\to b \bar{b}$, which is proportional to the Heaviside function $\Theta(E-E_0)$, so this particular process ...
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Symmetry breaking and superpositions? [duplicate]

Let the Hamiltonian $H$ be invariant under the symmetry $U$ such that: $$U H U^\dagger = H \, .$$ Consider a bias of ground states $\{\left|GS,n\right>\}$. It is often said that if $\left|GS,n\...
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Spontaneous Symmetry Breaking Field - Physical Significance.

One way to define spontaneous symmetry breaking (SSB) is as follows (Morandi, Ercolessi and Napoli, 2001; my wording): We can define SSB as occurring when: $$\lim_{h\rightarrow 0} \lim_{N\...
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Substitute for QFT by Weinberg [duplicate]

My professor asked me to read chapter 19 on broken symmetries from Steven Weinberg's Quantum theory of fields, but I seem to not grasp the content at all. Is there any other substitute that is ...