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.

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Renormalization of linear sigma model fixing the Vacuum Expectation Value (VEV)

In the linear sigma model $$ \mathcal L = (\partial_{\mu} \phi^i)^2 + \frac 12 \mu_0 (\phi^i)^2 + \frac{\lambda_0}{4} ((\phi^i)^2)^2 ,$$ the symmetry is broken around the vacuum expectation value (VEV)...
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Why in spontaneous symmetry breaking do we only look at the scalar fields? [duplicate]

In all the examples of SSB in our course/the books (even in our SUSY course) we have just looked at minima of the scalar potential. Why do we restrict ourselves to the scalars, why not also minimise ...
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Deriving masses after spontaneous symmetry breaking with a field in a peculiar representation

I am attempting to break the Pati-Salam group $SU(4)_{c'} \times SU(2)_L\times SU(2)_R$ with a field $\psi$ that fits in the following representation: $(4,\bar 2,1)$. My objective is to derive the ...
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The Higgs mechanism in a quiver gauge model

I've been reading chapter 20 in Peskin and Schroeder about the Glashow-Weinberg-Salam Theory for a $U(1)$ gauge symmetry with gauge coupling strengths $g$, and a complex scalar $\phi$, specifically ...
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Goldstone theorem in Schwartz

On page 566, Schwartz’s QFT book, to see the $\pi$ is the Goldstone boson, it reads: $$J^\mu=\frac{\partial L}{\partial(\partial_\mu \pi)} \frac{\delta \pi}{\delta \theta}=F_\pi \partial_\mu \pi \tag{...
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Higgs vev: diagonal or not?

I've read at different, places (for instance, this answer) that you can choose the vev of an adjoint Higgs to correspond to a generator of the Cartan subalgebra of the symmetry you are trying to break....
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Symmetry breaking and higgs representation

I was wondering if there is a criterion for the representation the Higgs should change under or if it's a case by case scenario. For instance, electroweak symmetry breaking is done with a higgs in ...
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Is a pseudo-Goldstone boson always a pseudoscalar particle?

There are several examples of pseudo-Goldstone bosons which are CP-odd particles, such as the pion, as well as many axion-inspired models. If we invert the logic, Are all pseudo-Goldstone boson of ...
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Meaning of a state breaking e.g. $\rm U(1)$ symmetry

I am reading a paper in which the authors discuss many-body states and describe them in terms of their symmetries, but do not know what is meant by e.g. a state breaking $U(1)$ symmetry. The ...
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Two-point functions don't signal spontaneous symmetry breaking?

I am aware that when some operator $\phi_n(x)$ which transforms nontrivially with respect to some symmetry group acquires a VEV, it signals the spontaneous breakdown of a particular symmetry, since ...
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De Almeida-Thouless line and spin glass in the Hopfield network

From the SK model, the Almeida-Thouless line appears to divide the stable paramagnetic phase and unstable spin-glass phase in the presence of an external magnetic field. However, in the case of a ...
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Gauge fixing, Lorentz invariance and the metric of the Hilbert space

Context In the first $3$ minutes of this video lecture (based on the presentation here) on the subject matter of Goldstone theorem without Lorentz invariance by Hitoshi Murayama, he recalls that the ...
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Vacuum Manifold of $U(1)$ theory and Goldstone theorem

I want to know if my understanding of the Goldstone theorem is correct. What I know is that the number of Goldstone is equal to the rank of $G/H$ where $G$ is the symmetry of the Lagrangian before ...
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Why does probing Higgs self coupling provides information on *dynamics* of Electroweak Symmetry Breaking?

Why does probing Higgs self coupling provides information on dynamics of Electroweak Symmetry Breaking ? Also, Why does probing Higgs self coupling provides information whether Higgs boson is ...
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Higgs mechanism and spontaneous symmetry breaking

I'm really confused about spontaneous symmetry breaking and the Higgs mechanism. I've searched for other answers but I couldn't still resolve all my doubts. I also understand that I'm asking a lot of ...
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In spontaneous symmetry breaking, can we define quanta of $\phi$ field?

A simple Lagrangian where spontaneous symmetry breaking is possible is that of a real scalar field $\phi$ with quartic interaction $$\mathcal{L}=\frac{1}{2}(\partial\phi)^2-\frac{\mu^2}{2}\phi^2-\...
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Why does a tube of frozen yogurt heat at only one end in a microwave oven?

The tubes of yogurt have a shell of thin plastic, with a single lengthwise seam and sealed at each end symmetrically apart from a small cut to initiate tearing at one end. They are of internal length ...
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Indications on the axion symmetry breaking scale

The production of cold dark matter axions can be provided for by multiple mechanisms which in turn depend on whether the breaking of the $U(1)_{pq}$ symmetry occurs before or after the inflationary ...
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Inversion symmetry in 2D materials

Transition metal dichalcogenides (TMDs) are composed of three atomic planes and often two atomic species: a metal and two chalcogens. The honeycomb, hexagonal lattice has three fold symmetry and can ...
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How can QED have degenerate vacua without superselection?

This question is based on Andrew Strominger's lecture on the IR structure of field theories, in particular Section 2.11 The usual story with spontaneous symmetry breaking is a follows. You have ...
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Breaking of spherical symmetry in crystals

I have been reading the book Transition Metal Compounds, and when the author begins to discuss transition metals in crystals, they state When we put a transition metal ion in a crystal, the ...
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What are the differences and similarities between Quantum synchronization and time-crystalisation?

I am learning about Quantum synchronization and read [1,2] on Sunday, which are about many-body bosonic systems. I understand that what happens when the system synchronizes is that all the particles ...
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What are the differences and similarities between Quantum synchronization and Bose condensation?

I am learning about Quantum synchronization and read [1,2] yesterday, which are about many-body bosonic systems. I understand that what happens when the system synchronizes, is that the destruction ...
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Why can we minimize the potential as just a function of a single numeric variable in spontaneous symmetry breaking?

In the discussion of spontaneous symmetry breaking one starts with considerations about the classical vacuum, defined as the field configuration $\Phi(x)$ which minimizes the energy encoded in the ...
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Why does symmetry spontaneously break? [closed]

Why does symmetry spontaneously break? For example,in the case of the mexican hat potential, as far as I can tell, a particle that is at the unstable equilibrium ought to be able to continue staying ...
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What is the density of Higgs Boson at different places

I understand that the Higgs Field is everywhere, but I don't have a feel for the density, or number, of Higgs Bosons in an area - say 1 cubic metre. Is there 1 mole of HB for every mole of quark in a ...
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Vacuum expectation value (VEV) of a Gauge theory - Spontaneous Symmetry Breaking (SSB) - Higgs Mechanism

I am dealing with a sort of scalar QED with a term of SSB \begin{equation} \mathcal{L}=\left|D_{\mu} \phi\right|^{2}-\frac{1}{4}\left(F_{\mu \nu}\right)^{2}-V\left(\phi^{*} \phi\right) \end{equation} ...
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Electric charge operator and the charges of $W^\pm$ mesons

In Ch.20 of the textbook An Introduction to Quantum Field Theory by Peskin and Schroeder, when discussing spontaneous symmetry breaking in SU(2)$\times$U(1) in the context of Glashow-Weinberg-Salam ...
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Peskin Schroeder Higgs mechanism for an $SU(3)$ gauge theory with a scalar field $\varphi$ in the adjoint representation

In Peskin Schroeder pag.696 a Higgs mechanism for an $SU(3)$ gauge theory with a scalar field $\phi$ in the adjoint representation is presented. The covariant derivative of $\phi$: $$ D_{\mu}\phi_{a} =...
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Why can't we interpret the W, Z bosons as massive vector bosons not arising from a gauge theory? [duplicate]

The standard story goes as follows: gauge bosons cannot have a mass term because it would break gauge invariance in the lagrangian. This is clear, but why can't we just have massive vector bosons ...
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Why are the masses of $W^{\pm}$ and $Z^0$ different?

We know that through the Higgs phenomenon, the weak bosons become massive. In our Lagrangian the $W^\pm$ boson is usually defined as $\frac{1}{\sqrt{2}}(W^1_\mu\mp iW^2_\mu)$ and $Z^o$ is usually ...
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Are gravitons Goldstone bosons?

This question is inspired by Are Photons Goldstone Bosons?. And recently in Generalized Global Symmetries, photon was interpreted as Goldstone boson for generalized symmetry (see also my answer for ...
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When the EM vector field is given a mass by Higgs mechanism, why isn't this equivalent to a massive photon?

In chapter 6 of Classical Theory of Gauge Fields (Rubakov), we are presented with a scalar field $\phi$ coupled to the electromagnetic vector potential $A_\mu$. In this Lagrangian there is a quartic ...
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How is mass-energy conserved during false vacuum decay?

If we live in the false vacuum, there is a probability that spontaneous vacuum decay could occur: quantum fluctuations could result in a bubble of true vacuum that expands at the speed of light. In ...
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Higgs mechanism and phase transition

Generally speaking, phase transitions divide into two types: First order and second order. To me, Higgs field's SSB sounds like a second-order one though I don't know the dependency of Higgs field's ...
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Do expectation values of quantum fields behave like classical fields?

A famous result in quantum mechanics is Ehrenfest's theorem which states that the expectation values of observables are governed by the classical equations of motion. Does a similar statement hold ...
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Coupling constants in sponataneous symmetry breaking

In an extended standard model we have an additional triplet Higgs field to the complex doublet. The fields are given below $ \Phi = \begin{pmatrix}\phi^+\\\frac{1}{\sqrt{2}}(v+h^0+i\phi^0) \end{...
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Higgs mechanism and gauge symmetry

In the case of massive bosons of weak interaction we have Higgs mechanism to save the symmetry. I do not see how with Higgs the symmetry is preserved? Because the mass term is what gives us problems ...
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How come Goldstone boson, PQWQ axion, be able to have mass at all?

Quote: Goldstone's theorem: For every spontaneously broken continuous symmetry, there is a massless particle created by the symmetry current. However, under $U(1)_{PQ}$ symmetry, I read that PQWW ...
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Higgs Yukawa coupling explicitly violating chiral symmetry

I'm pretty confident that I'm misunderstanding something here. The Yukawa coupling that couples the Higgs field to fermions can be written something like: $$ \lambda \bar L H e_r + h.c., $$ where $L,...
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Why Higgs field need hypercharge to work?

I know that photon and gluon don't have any hypercharge so they can zip through higgs field at speed of light while left and right handed particles seems to communicate with these hypercharge, so then ...
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Conserved currents in the Standard Model

As we know, the gauge bosons $W^{\pm}, Z$ and $\gamma$ couple to currents in the Standard Model. Now my question is are these currents conserved? I mean, there is no doubt about the electromagnetic ...
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Is there SSB in IQHE?

The Wikipedia page on FQHE mentions that the discovery of FQH states is significant partly because it shows the limits of Landau's symmetry breaking theory, since different FQH states all have the ...
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Layman's questions about Supersymmetry

Please help me with two very silly questions. Assuming supersymmetry is correct, why don't we observe the superpartners of the Standard Model particles at ordinary energies? Why do we have to search ...
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About the spontaneous breakdown of an anomalous symmetry

If a global symmetry is anomalous, classically it is still possible to talk about spontaneous breakdown of that symmetry. In particle physics, do we have such an anomalous symmetry (or symmetries) ...
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Why is the Mermin Wanger theorem not considered for superconductors in 2D?

Several papers set up a model of fermions in 2D and calculate superconducting $T_c$, e.g.: https://arxiv.org/pdf/1808.08635.pdf https://arxiv.org/pdf/1406.1193.pdf https://www.pnas.org/content/pnas/...
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One spin-1/2 particle in B field in a 3D harmonic potential (Part II)

Consider a spin-1/2 particle in a magnetic field (say in z direction) and in a harmonic potential. For the 3D harmonic oscillator component, The Hamiltonian $H_1= \frac{p^2}{2m}+\frac{1}{2}m\omega ^2r^...
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Fate of acoustic phonons in incommensurate charge density wave states?

In most standard exposition of (the mean-field theory of) charge density wave (CDW), phase and amplitude fluctuations are introduced as the collective excitations. Kohn anomaly in the acoustic phonon ...
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Normal force of particle residing on cone apex

By reading Norton dome "proof" about non-determinism of Newton laws, i've started to think about how much Norton system is physical at all. Let's push it to the limits. Let's say we have vertical cone ...
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Resources to understand the Higgs boson

I have to do a presentation about the Higgs boson, covering topics such as the problems with the standard model without Higgs, particle masses not being compatible with gauge symmetry and how it is ...

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