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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Why are photons massless? [duplicate]

I am trying to understand, from the QFT perspective, why photons are massless. Let's consider the following Lagrangian for a massive U(1) gauge boson $\mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+m^2A^...
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Why doesn't broken inversion symmetry imply piezoelectricity?

To see piezoelectricity in a crystalline material, you must have a crystal symmetry which is non-centrosymmetric (i.e. broken inversion symmetry). The reverse is almost always true (i.e. broken ...
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Why are non-perturbative solutions important and how to take them into account?

I am guilty of studying physics with an almost complete focus on the mathematical constructions (together with the motivating physical premisses) and ignoring the semantic physical intuition, which I'...
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QED breaking of parity invariance

QED is invariant under P,T,C for the Lagrangian containing operators of dimension equal or smaller than 4. I was wondering, what are the possible parity-breaking terms in QED with dimension smaller or ...
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Permanent magnets - why spontaneous symmetry breaking?

I am not a physicist. I'm curious about the cause of permanent magnetism in ferromagnetic materials. So far, I have formed the impression that a macroscopic net magnetic dipole moment is formed from ...
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Are all particles massless before supersymmetry breaking?

I am having troubles to understand the breaking mechanism in a supersymmetric theory. There is said that a particle and its superparticle have the same mass. Since no superpartners have yet been found,...
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Are the particles in electroweak SSB composite?

The energy scale of a universe containing the electroweak interaction and the Higgs field only is the average energy of the fields $W^1, ​​W^2, W^3$, $B$ and the Higgs field. If electroweak bosons ...
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Is Norton's dome valid (or does $\frac{d^2 \vec{p}}{dt^2} = \vec{0} \implies \frac{d^n \vec{p}}{dt^n} = \vec{0} \ \forall \ n > 2$)?

I came across Norton's dome and I don't agree that it proves anything. First, here's an obviously ridiculous and completely nonsensical example that I constructed from thinking about simple harmonic ...
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What were the $r$ and $n$ of $\theta$s (Polchinski String theory section 8.6 page 265)?

In the Polchinski String theory section 8.6 page 265 In generic backgrounds, all the $\theta$s are distinct and the only massless vectors are the diagonal ones, $i = j$. The unbroken gauge group in ...
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If we had a Higgs triplet with hypercharge $Y=1$, would we get three Higgs bosons?

In the Standard Model, the Higgs field is a doublet of SU(2) and hypercharge $Y=1/2$. We have four real scalar degrees of freedom (since $H$ is a complex doublet); three of these get "eaten" ...
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Are there any theories of the beginning or the end of the universes where all fundamental symmetries would be violated?

There are theories trying to explain the origin of the universe (such as inflationary models) and also theories that try to predict how will the universe end (like the "big freeze", the &...
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Nonlinear symmetry realization: what is it for and caveats?

I have several doubts regarding the nonlinear realization of a spontaneously broken symmetry and hope they are appropriate to be grouped, and I appreciate any insights. Consider the group breaking ...
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$SU(3)$ and $SU(3)\times SU(2)\times U(1)$ Symmetry Breaking [duplicate]

For my master's project I was doing spontaneous symmetry breaking in which I covered U(1), SU(2), SU(2)×U(1) symmetry breaking. My supervisor has said that for the project this much is enough. But now ...
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Symmetry restoration at high temperature

Weinberg in his famous article https://doi.org/10.1103/PhysRevD.9.3357 discusses how finite-temperature effects in a renormalizable quantum field theory can restore a symmetry which is broken at zero ...
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Could there be some process or event that would make the universe to be Lorentz non-invariant?

As far as we know the universe is invariant under the Lorentz symmetry and does have many other fundamental symmetries from which we derive the fundamental laws of physics. But could there be any ...
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References to superpositions of vacua states, for SSB

I would like to read more about this subject, about having an unbroken symmetric superposition of the vaccua (minimum energy state), instead of directly chosing one, for computing SSB as my teachers ...
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Vacuum Transitions and Lorentz Symmetry Breaking

There are many "bumblebee" models 1, 2 where Lorentz invariance is violated usually resulting from a local vector or tensor field acquiring a nonzero vacuum expectation value We do not know ...
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Symmetry breaking in near free electron?

In 1D lattice, if we consider a near-free electron model, ie. $$\hat{H}=-\hat{\psi}^{\dagger}(x)\frac{\nabla^2}{2}\hat{\psi}(x)+V(x)\hat{\psi}^{\dagger}(x)\hat{\psi}(x)$$ where $V(x)$ is a periodical ...
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Quantum Time Crystals

I am not sure I appreciate the implication made by Wilczek here: I definitely see how the expectation value for $\dot\phi$ becomes zero for an energy eigenstate $\Psi_E$ but I do not see what he is ...
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Is the free spectrum of a theory, way above the symmetry breaking scale, massless?

I have asked a similar unanswered question, focused on different aspects, here. My intuition regarding statements frequently made about this issue is that, if a theory contains a breaking pattern $G \...
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Could the Lorentz symmetry be theoretically broken in vacuum?

In this paper 1 which considers the possibility that the Lorentz symmetry could be broken, at page 4-5 the author says: "We now introduce a Higgs sector into the Lagrangian density such that the ...
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Example of the symmetry breaking and the unchanged charge commutation in the current algebra

In the current algebra by J.D. BJORKEN, https://doi.org/10.1146/annurev.ns.18.120168.001305 discussed the origin of the current algebra. The paper said Gell-Mann In attempting to interpret in ...
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How could negative $W$ "eat" the positive Goldstone bosons $\phi_1$ and $\phi_2$?

In the Standard Model, the Higgs field is $\Phi=\left(\begin{array}{c}\phi^+\\\phi^0\\\end{array}\right)=\frac{1}{\sqrt{2}}\left(\begin{array}{c}\phi_1+i\phi_2\\\phi_3+i\phi_4\\\end{array}\right)$. ...
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Am I correctly interpreting Eq. (4.1) from Erick Weinberg's book, "Classical Solutions in Quantum Field Theory"?

I have been studying Erick Weinberg's book, "Classical Solutions in Quantum Field Theory", and I am confused about Eq. (4.1) from p. 58. I believe my issue of confusion is notational, and I ...
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What does the Spontaneous Symmetry Breaking with Higgs Mechanism imply effectively?

Suppose it is understood how the Spontaneous Symmetry Breaking work mathematically to give masses to Fermions through Yukawa Interactions and to Gauge Bosons via Higgs Mechanism. In this case, my ...
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Goldstone Modes, Galilean Symmetry, and Negative Excitations in Fermi Gas

Considering the centrality of Goldstone quasiparticles in condensed matter theories, I was wondering if the converse of the theorem might also be true: Does the existence of a gapless excitation imply ...
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Confusion about symmetry spontaneous breaking in a simple model

Hamiltonian and symmetry I was learning about the symmetry spontaneous breaking (SSB), but confused by this simple minima model$$H=E_0\sum_{i=1}^3|i\rangle\langle i|+J\left(|1\rangle\langle 2|+|2\...
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Entropy of a spin spontuaneous simmetry breaking?

The Shannon entropy of a probability mass function is $$H(S) = -\sum_s p(s)\log_2 p(s),$$ where the sum runs over all the configurations $s$. If a system $S$ stays half of the time in the ...
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Non-linear group representations

Different representations of the Lorentz group in infinite-dimensional vector spaces are related to the types of particles (classification by spin and mass). These representations are linear. Are non-...
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Identifying mesons with Goldstone modes

In QCD, due to the work of ‘t Hooft and Vafa-Witten, we know that confinement implies chiral symmetry breaking (David Tong’s gauge theory notes have a clear discussion of this). It is then said that ...
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Are fields $B_{\mu}$, $W_{\mu}$ only before electroweak symmetry breaking (EWSB), and $\gamma$, $Z$, $W^{\pm}$ after it?

In the context of Lagrangian of Standard Model of particle physics, is the usage of the notation with $B_{\mu}$ and $W_{\mu}$ before electroweak symmetry breaking (EWSB), and the notation with $\gamma$...
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Why is the electron massless before interaction with the Higgs field?

Can't the electron have a mass before electroweak symmetry breaking, which is then just modified by its interaction with the Higgs field, instead of gaining all its mass this way? Apparently other ...
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Coset construction for space-time symmetry breaking: how is the covariant derivative built?

I am currently learning how to build effective field theories for Nambu-Goldstone modes (NG modes) by using the coset construction formalism. I essentially follow 2 reviews: For the breaking of ...
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Gaussian Propagator and Symmetry Breaking

Regarding the propagator $\mathcal{G}(k,i\omega,r)$ of a Euclidean scalar real Gaussian quantum field theory $$\mathcal{Z_0}=\int\mathcal{D}[\phi]e^{-\mathcal{S}[\phi]}$$ $$\mathcal{S[\phi]}=\int d{\...
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How (if) are the spontaneous symmetry breakings of the Higgs field at different locations correlated?

I don't know what it is, but no one seems to be able to give a satisfactory answer about the how of the mass generation in the Higgs mechanism. The amplitude of the Higgs field falls into the rim of ...
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Intuition/Motivation behind necessity of Spontaneous Symmetry Breaking to generate massive gauge bosons

In field theory textbooks, it is shown that while any gauge invariant Lagrangian must involve massless gauge fields, to obtain massive gauge bosons, we must postulate the existence of a Higgs scalar ...
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What Lorentz symmetries do electric and magnetic fields break?

When we turn on an external (non-dynamical) electric or magnetic field in (3+1)-dimensional Minkowski space we break rotational invariance because they pick out a special direction in spacetime. Does ...
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Relation between Spontaneous Symmetry Breaking and Renormalization Group

I have two different pictures in my head of how a phase transition occurs, but I am not sure of the relation between these two pictures. SSB: Our theory has a global symmetry and when the parameters ...
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How does the Nambu-Goldstone mode explain the absence of parity doubling?

I've been doing some reading about chiral symmetry breaking since it was not touched in my particle physics course I found these slides As explained in the above link, if we take $|\psi \rangle$ as ...
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"Domain wall" from continuous symmetry

For a discrete $\mathbb{Z}_2$ symmetry for instance, in some patches of the Universe, it can spontaneously breaks $\mathbb{Z}_2$ and goes in the "right" minimum, while in some others patches ...
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Is this asymmetrically frozen ice cream an example of symmetry breaking?

Today I noticed my ice cream had frozen in an asymmetric pattern because I left it resting at an angle on the fridge. I'm wondering if this is analogous to the concept of symmetry breaking as used in ...
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Frustrated classical field theory

The frustrated Ising model (see e.g. this answer) is an example of a system that shows no unique ground state and many metastable states (its "energy landscape" is extremely complex). ...
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Statistical physics of broken symmetry state?

If we are considering a system, like a paramagnet, above its critical temperature $T_c$ we can statistically describe it using a canonical ensemble: $$ \langle A \rangle = Tr\left[ \rho A \right]; \...
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How can the Higgs Field have low energy but high vacuum expectation value?

I'm not a math student, I'm just curious as to know why and how can a vacuum be more stable with high Vacuum expectation value than 0 vev. A similar question would be what does it mean when the EM and ...
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System of particles with spin & symmetry breaking

I was solving an exercise in which I had to find how the entropy of a system of N (assuming distinguishable) particles with spin changes when the temperature $T\rightarrow0$ and $T\rightarrow \infty$. ...
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In an $SO(10)$ GUT, how many gauge fields acquire masses that are above the electro-weak scale?

The $SO(10)$ group is spontaneously broken down into the Standard Model gauge group at around $10^{16}$ GeV and the electroweak scale is ~246 GeV. I think there should be 45 gauge fields predicted by ...
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Have magnetic monopoles been predicted to have been produced in other cases than those of symmetry breaking in GUTs?

Also, what other configurations are magnetic monopoles theorized to exist in? (such as black holes, monopole walls etc.)
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What related massive/massless degrees of freedom and the generators of a field?

A lecturer has stated that it is possible to determine the number of massive and massless degrees of freedom from the known generators of a $SO(3)$ field and a given v.e.v. In the given example, the ...
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Is the early universe cosmology phase transition thermal or quantum? WHY?

In this question How does SSB happen?, one of the answers assumes the nature of the early universe phase transition to be thermal. I need to know why can't such phase transition be a quantum phase ...
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Does the number of broken generators in SSB depend on the choice of VEV?

I take the Lagrangian, $$\mathcal{L}=\frac{1}{2}\partial_\mu \phi^T\,\partial^\mu\phi\,-\, \frac{1}{2}\mu^2\phi^T\phi-\frac{\lambda}{4}(\phi^T\phi)^2~,$$ where $\phi=(\phi_1,\,\phi_2,\,\phi_3)$ (real ...
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