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Questions tagged [goldstone-mode]

The Goldstone mode is a massless quantum excitation arising in systems with spontaneous breaking of continuous symmetry. That is, the Noether symmetry currents are conserved, but the vacuum is not invariant under the symmetry, so the symmetry is not immediately apparent, realized non-linearly. Goldstone Modes are found throughout physics, with some celebrated examples stemming from the Higgs Mechanism.

The Goldstone mode is a massless quantum excitation arising in systems with spontaneous breaking of continuous symmetry. That is, the Noether symmetry currents are conserved, but the vacuum is not invariant under the symmetry, so the symmetry is not immediately apparent, realized non-linearly.

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In what sense do Goldstone bosons live in the coset?

Goldstone's theorem says that if a group, $G$, is broken into its subgroup, $H$, then massless particles will appear. The number of massless particles are given by the dimension of the coset, $G/H$. It is then often said that the Goldstone boson's…
JeffDror
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The meaning of Goldstone boson equivalence theorem

The Goldstone boson equivalence theorem tells us that the amplitude for emission/absorption of a longitudinally polarized gauge boson is equal to the amplitude for emission/absorption of the corresponding Goldstone boson at high energy. I'm…
cnzz601
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Schwartz's and Zee's proof of Goldstone theorem

In Refs. 1 & 2 the Goldstone theorem is proven with a rather short proof which I paraphrase as follows. Proof: Let $Q$ be a generator of the symmetry. Then $[H, Q] = 0$ and we want to consider the case in which $Q | 0 \rangle \neq 0$. As a…
MrRobot
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Goldstone's theorem, symmetry breaking and the Heisenberg model

I'm currently researching symmetry breaking and Goldstone's theorem for a project in my third year of my theoretical physics degree. So my knowledge isn't from a formal teaching but my own research. I began with trying to understand Goldstone's…
Horro
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Vacuum Degeneracy for Massless Free Scalar Field

I am wondering how to explicitly see the vacuum degeneracy for a free massless scalar field, described by the action $$S = -\frac{1}{2}\int d^4x\,(\partial\phi)^2.$$ This action is invariant under the nonlinearly realized shift symmetry…
anon123456789
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Skin depth and Mermin-Wagner theorem

I recently became aware of the Coleman-Mermin-Wagner theorem presented in [1802.07747] for higher-form symmetries and I have a question about how it might be applied to electromagnetism. The theorem states: continuous $p$-form symmetries in $D$…
user105620
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About Itzykson and Zuber's proof of Goldstone's theorem

In chapter 11-2-2, I&Z discuss Goldstone's theorem. They start by claiming that if an operator $A$ exists, such that $$ \delta a(t) \equiv \langle 0| [Q(t),A]|0\rangle \neq 0 \tag{11-30} $$ the symmetry is spontaneously broken. In Eq. (11-31), they…
ersbygre1
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Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance

I am reading an article Unified Description of Nambu-Goldstone Bosons without Lorentz Invariance, arXiv:1203.0609, by Watanabe & Murayama. It gives a proof on the counting of Nambu–Goldstone bosons without Lorentz invariance. I am trying to derive…
soliton
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Why phonons are Goldstone modes?

I read this in the lecture notes by David Tong: "Gapless excitations often dominate the low-temperature behaviour of a system, where they are the only excitations that are not Boltzmann suppressed. In many systems, these gapless modes arise from…
Iris Allevi
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Goldstone theorem for classical and quantum potential

Consider a quantum theory $$\mathcal{L}(\phi^a) = \mathcal{L_{kin}}(\phi^a)-V(\phi^a),\tag{11.10}$$ depending on any type of fields $\phi^a$. The VEV of this theory are constant fields $\phi_0^a$ such that $V(\phi^a)$ is minimized and if some…
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Factoring a the exponential form of a group element of a Lie group, using subgroups

I am working on non linear realization of Goldstone bosons, as is done by Weinberg in section 19.6 of Quantum theory of fields, volume II. We have a real, compact and connected Lie group $G$ with as subgroup $H$. Let $t_a$ be the generators of $H$,…
Martin Johnsrud
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Measuring and calculating free quark masses

Particle data book contains masses of the free quarks. I wonder, how do experimentalists determine the masses of the free quarks even though they are trapped inside hadrons (except perhaps in quark-gluon plasma)? Can quark masses be theoretically…
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Confusion of the Proof of Goldstone Theorem in QFT

Context I found many proof of the symmetry breaking is the following: Let $\langle \delta \phi(x) \rangle$ be the corresponding symmetry transformation w.r.t. the charge $Q = \int d^Dx\; J^0(x)$. $\langle \delta\phi(p=0) \rangle = \int d^Dx\;…
Steven Chang
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Why are there no Goldstone modes in superconductor?

Usually, the absence of Goldstone modes in a superconductor is seen as an example of the Anderson-Higgs mechanism, related to the fact that there is gauge invariance due to the electromagnetic gauge field coupled to the charged electrons. However,…
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Global symmetries QCD goldstone bosons

Beside the local $SU(3)$-Color-symmetrie The QCD Lagrangian also has global symmetries: $$L_{QCD}=\sum_{f,c}\bar{q_{fc}}(i\gamma^\mu D_\mu - m ) q_{fc} - \frac{1}{4}F^a_{\mu \nu} F^{a \mu \nu} $$ $SU(2)_V$ Isospin, since $m_u \approx m_d$, the…
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