# 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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### 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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### 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 ...