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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$\text{SU}(5)$ GUT Higgs sector and symmetry breaking

The Higgs sector of minimal $\text{SU}(5)$ GUT consists of scalar fields in two representations, a $\mathbf{24}$ and a $\mathbf{5}$. All the $\mathbf{5}$ non-derivative terms form the potential $V(\...
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Spontaneous symmetry breaking confusion

I was reading the spontaneous symmetry breaking in the case of double well . And i come to the following statement "When there is a degeneracy, the ground state no longer has to obey the symmetry ...
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Confusion about spontaneous symmetry breaking rod example

I was reading a book on QFT and the example he uses to make an analogy of spontaneous symmetry breaking in QFT is that of the rod where a compressive force is applied on the top surface of the rod ...
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Particle interpretation for Fields and (non) vanishing VEV

I have some questions about the first part of the answer by Arnold Neumaier dealing with the interpretation of VEV (vacuum expectation value). Let me quote the parts I would like to understand better: ...
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Spontaneous Symmetry Breaking vs Addition of 'Mass terms' by hand [duplicate]

Let consider an $SU(2)$ doublet of bosons $\Phi =(\phi_A, \phi_B)$ which is described by the Lagrangian $$L = (\partial_{\mu}\Phi)^{\dagger}(\partial_{\mu}\Phi) +a^2 V(\Phi^{\dagger} \Phi) -\frac{\...
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Chiral symmetry breaking and appearance of hadrons (from Schwartz's QFT book)

Matthew Schwartz's QFT book mentions following thing, but I cannot understand the logic Spontaneous symmetry breaking of $SU(2) × SU(2)$ happened 14 billion years ago, when the temperature of the ...
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Vacuum expectation values (VEV) and Spontaneous symmetry breaking

I have a basic question about spontaneous symmetry breaking for theory with one complex scalar field $\phi= \phi_1 +i \phi_2$ with Lagrangian $$ \mathcal{L}=\partial _\mu \phi ^*\partial ^\mu \phi +\...
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In Higgs context, do false vacuum hypothesis imply that true vacuum is *higher* (not lower)?

In theories of false vacuum for Higgs potential, the Higgs field would be currently in an instable false vacuum and would later evolve in a true vacuum, with a lower potential value. Would this true ...
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Symmetry breaking for 4 scalar fields

So I've been trying to get familiar with concept of symmetry breaking with minimal experience with field theory and I've got stuck on, I think, a simple problem. Let's consider four scalar fields $\...
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Field “Expansion”/Shift in Spontaneous Symmetry Breaking

I currently take a lecture called Symmetries in Particle Physics. And when talking about the spontaneous breaking of a global continuous symmetry the lecturer said that the field is expanded around ...
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Spontaneous symmetry breaking with 1 massive scalar but three unbroken generators?

Consider some theory of four real scalar fields, $\phi_1$, $\phi_2$, $\phi_3$ and $\phi_4$, that is invariant under a global $$SO(4)\cong SU(2)_L\times SU(2)_R$$ symmetry. We can rewrite the real ...
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Are Spring Oscillations Goldstone Modes?

When considering a spring-like object, it seems almost intuitive that it would be "springy", i.e., harmonically oscillate. However, these oscillations occur at a macroscopic scale, unlike ...
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Is there any possibility of manipulating the Higgs field, and if so, what effects would we see?

These are questions asked from a perspective of "what if" according to current theory. If the Higgs field is the source of mass for (most) elementary particles, and the unique property of ...
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Peskin & Schroeder about spontaneous symmetry breaking

I am confused about how Peskin & Schroeder derive the matrix (21.39): \begin{equation} gF^a_{\ \ i}=\frac{v}{2} \left(\begin{array}{ccc} g & 0 & 0 \\ 0 & g & 0 \\ 0 & 0 & g ...
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Spontaneous symmetry breaking of $SU(2)$ in real and complex scalar fields

Here is a toy problem whose aim is to help me understand breaking global symmetries into subgroups and under which occasions that is possible. My question is: does a field being real or complex affect ...
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Time translational symmetry breaking

I have heard of time translational symmetry, which refers to the law of conservation of energy. Time crystals break time translational symmetry. I read on Wikipedia that it only breaks discrete-time ...
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What are the two different $\mathbb{S}^n$ in the construction of the homotopy group $\pi_n(\mathbb{S}^n)$ that classifies topological defects?

According to Mukhanov's Physical Foundations of Cosmology, Homotopy groups give us a useful unifying description of topological defects. Maps of the $n$-dimensional sphere $\mathbb{S}^n$ into a ...
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Meson operator treated as an elementary field in effective action?

I have seen in many papers, with this as the earliest example I can find, that the meson chiral order operator $M_j^{\,\,\,i}(x)=\overline{\psi}^i(1+\gamma_5)\psi_j(x)$ is treated as an elementary ...
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Could some kind of vacuum decay modify the most fundamental laws of physics?

A false vacuum is a hypothetical vacuum that is not actively decaying, but somewhat yet not entirely stable ("metastable"). It may last for a very long time in that state, and might ...
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What is meant by spontaneous symmetry breaking?

What is meant by spontaneous symmetry breaking? I am really confused about this topic. In my text book it says: "At a continuous phase transition, the slope of the free energy curve changes ...
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Goldstone bosons in soft limit

There's interesting statement about amplitude of Goldstone bosons: I wanna to understand simple argument for statement of vanishing of amplitudes in the single scalar soft limit. In principle, it is ...
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Is it correct to discuss “Symmetry” and “Breaking of symmetry” on equal footing? [closed]

My Background: A senior Undergraduate Student With no Idea of Field Theory Whatsoever. I am looking for a very general and natural answer to my question. I noticed that Symmetry is not something ...
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Proof of Mermin-Wagner Theorem

There are many presentations of the proof of the Mermin-Wagner theorem in many different contexts (which talk about quantum vs. classical, existence of unique Gibbs measure or non-zero mean ...
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On Goldstone fermions / goldstino: SUSY breaking

There are statements about Goldstone fermions, or goldstino, seem confusing to me. (1) Goldstone boson requires a continuous symmetry spontaneously broken. Does Goldstone fermion imply continuous SUSY ...
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Supersymmetry non-breaking $\iff$ no “Goldstone fermion”?

In Supersymmetry and Morse Theory (1982) by E Witten, Concern whether the supersymmetry is broken by checking whether $$ Q | 0 \rangle=0 $$ exists or not --- Witten said: SUSY breaking: A solution ...
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Correlation function and spontaneous symmetry breaking

Let's look at ferromagnetic system as an example. The correlation function is defined: $$G(r,r_{0})=\langle(m_{r_{0}}-\langle m_{r_{0}}\rangle)(m_{r}-\langle m_{r}\rangle)\rangle=\frac{1}{r^{p}}e^{-\...
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Higgs Lagrangian and massive/massless fields

In QFT yesterday we were talking about Higgs/SSB and mass terms in Lagrangian. Our professor wrote down some lagrangians and asked us to explain certain things and also if it is for massive or ...
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What is the value of electromagnetic coupling at the energy where it merges into electroweak couplings?

It is known that its zero-energy value is the fine-structure constant α, about 1/137.036. Various sources state that the running value is in the 1/129-1/127 range at the Z-boson energy (91 GeV). ...
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Non-extended and extended SUSY

What are the distinctions between Non-extended SUSY and Extended SUSY? (Is that just a non-extended SUSY has $\mathcal{N}=1$ while the extended SUSY has $\mathcal{N}>1$ ? Then there is no ...
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Violation of time reversal symmetry

Can anyone please provide me with an example of unperturbed Hamiltonian for a certain physical system, which has no time-reversal symmetry, the only condition is that the spectrum of unperturbed ...
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Will electromagnetism separate into electricity and magnetism as the universe cools down?

The electroweak force separated into the weak force and electromagnetism. So, will the electromagnetic force eventually separate into electricity and magnetism?
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What would it mean if symmetries are not fundamental at all?

In this paper 1 written by Joseph Polchinski, he seems to indicate that all symmetries of nature may not be fundamental: From more theoretical points of view, string theory appears to allow no exact ...
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Goldstone counting from symmetries and from the expansion in the Lagrangian

Goldstone theorem states that when a continuous symmetry is broken there is a massless mode for each broken generator. To exemplify the theorem, many references consider the complex scalar theory with ...
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Confusion on the proof of Goldstone’s theorem

I amd reading a proof Goldstone’s theorem in Zee's QFT book. On page $228$, Zee presents the proof as follows. The conserved charge $Q$ is given by \begin{equation} Q=\int d^D\vec{x}J^0(t,\vec{x}). \...
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Quark condensate and spontaneous symmetry breaking?

It is known the quark condensate $<\bar{\psi}^{i}_L\psi^j_R>=\sigma \delta^{ij}$($i,j$ are flavour indices ) breaks the symmetry group $SU(N_f)_L\times SU(N_f)_R$. Because it is only invariant ...
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Explicit breaking of conformal symmetry

I think of a relativistic conformal field theory as basically any theory which does not have a length scale. Say all particles are massless and all couplings are dimensionless. (I could really talk ...
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Is the value of the scalar components of the Higgs field known?

As I understand the relevant popular sources (example), since the end of the Electroweak epoch, the Higgs field became fixed in the whole known Universe. Thus, we are somewhere on the deep blue part (...
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VEV implying symmetry breaking, but unable to pick out specific subgroup?

Let's say we have a scalar theory with an $O(N)$ symmetry, for which the scalar fields $\phi_{nm}$ transform as a rank $2$ tensor. I can write down an action which spontaneously breaks the symmetry $$...
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Chiral Symmetry Breaking in Graphene

I am trying to understand chiral symmetry breaking in the context of graphene with Coulomb interaction ; I understand how to move from a tight-binding Hamiltonian to a field theoretic setting (2+1 QED ...
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For finite magnetic field B, the exact ground state of transverse Ising model still does not break the 𝑆𝑧→−𝑆𝑧 symmetry

In the comments of OP What is spontaneous symmetry breaking in QUANTUM systems? There is a statement by OP Xiao-Gang Wen saying "the ground state of transverse Ising model $$𝐻=−∑𝑆𝑧_𝑖𝑆𝑧_𝑗+𝐵...
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Is there any model or theory which predicts the existence of multiple vacua with different fundamental symmetries?

In certain models of string theory it is predicted that many vacua may exist. These vacua could be governed by different effective laws of low-energy physics resulting from different symmetry breaking ...
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Why are electric monopoles not interpreted as topological defects but magnetic monopoles are?

What explains this asymmetry between the electric and magnetic fields if both electric and magnetic monopoles exist? Can't Maxwell's equations be formulated to be symmetric between the two in the ...
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If symmetry breaking occurred at very high energies at the beginning of the universe, could our fundamental laws of physics have been different?

In some models of the beginning of the universe, like for example in chaotic inflation, space would stop expanding in some points, creating hubble volumes that could experience different spontaneous ...
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References on what kind of order does the integer quantum Hall effect exhibit

I'm looking for references to understand how exactly does the integer quantum Hall effect (IQHE) escapes Landau's symmetry breaking description. Any recommendations would be appreciated, thanks!
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Current conservation in presence of SSB: weak currents

The Standard Model SSB breaks the $SU(2)_W \times U(1)_Y$ to $U(1)_{EM}$. The Noether currents associated to the unbroken group are $J_{a,\mu} = \bar{\psi} \gamma_\mu \frac{\tau_a}{2} P_L \psi $ and $...
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What is the mass of the Goldstone boson sound wave?

Wolfe and N.H. Fletcher in the “Interactions between wind instruments and their players say that, in a flute “…after a few periods of the fundamental, the overtones become locked into exact harmonic ...
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What does a broken symmetry mean for the Lagrangian?

I am a little confused about symmetry breaking - in particular, what I see to be too different interpretations of it. First, what I have seen taken to be the definition of a broken symmetry - we start ...
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Spontaneous symmetry breaking without an order operator?

Spontaneous symmetry breaking occurs when there is a degeneracy in the ground state. Typically it is easiest to determine the degeneracy by finding some operator with a nonzero vacuum expectation ...
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Why don't $\rm SO(10)/Spin(10)$ or larger GUTs permit electron-pair decay?

$\rm Spin(10)$ unifies all left-handed fermions and anti-fermions, and all right-handed fermions and anti-fermions. And its Pati-Salam subgroup unifies quarks with leptons (SU(4)) and complements SU(...
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Why don't certain decorated domain wall constructions for SPTs lead to spontaneous symmetry breaking?

There is a construction of symmetry protected topological (SPT) states which roughly goes as follows. We start with a $d$-dimensional system with symmetry $\mathbb{Z}_2 \times G$ in the phase where ...

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