# 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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### 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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### 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 ...