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.
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Goldstone Theorem in Schwartz, follow-up
This is somewhat of a related question to
Goldstone theorem in Schwartz
and is related to equation 28.16 in Schwartz's QFT book.
One way to prove that
$$ \langle \Omega | J^\mu(x) | \pi(p) \rangle = i ...
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Unitary Gauge Removing Goldstone Bosons
The Lagrangian in a spontaneously broken gauge theory at low energies looks like
$$ \frac{1}{2} m^2 ( \partial_\mu \theta - A_\mu )^2 $$
and the gauge transformations look like $\theta \rightarrow \...
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Why are there no Goldstone modes in superconductor?
Usually, the absence of Goldstone modes in a superconductor is seen as an example of the Anderson-Higgs mechanism, related to the fact that there is gauge invariance due to the electromagnetic gauge ...
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Goldstone theorem for classical and quantum potential
Consider a quantum theory $$\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 ...
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Soliton and Goldstone boson
I'm learning Gross-Pitaevskii model. By spontaneous symmetry breaking one obtains Bogoljubov modes, which ensures Landau criterion. So those modes have two features, for one they are Goldstone bosons ...
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Existence of low temperature phase in 2-Dimensional XY-Model
I'm reading the lecture notes of David Tong on Statistical Field Theory, specifically chapter $4.4$ on the Kosterlitz-Thouless Transition. He considers the XY model in $d=2$ dimensions and states the ...
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Spectral function of superconductor in the BEC regime: how does Higgs mechanism affect the spectrum?
Consider the standard BCS theory but assume that the interaction energy $U$ that enters the definition of gap parameter (i.e. $\Delta = (U/N)\sum_k \langle c_{-k\downarrow} c_{k\uparrow} \rangle$, ...
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Goldstone bosons and spontaneous symmetry breaking in the complex triplet model
In the Standard model electroweak theory, the Higgs field is a complex doublet field, which couples to the $SU(2)$ gauge field. Suppose we replace the complex doublet with a complex triplet $\Sigma$:
$...
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Infinite conductivity, goldstone bosons and generalized voltage
Weinberg [1] has put forth an elegant argument (summarized in [2, Section 3.3] and at the bottom of the question), which suggests that the broken symmetry phase of any $U(1)$ gauge theory will be ...
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An issue with spectral representation in Coleman's proof of Goldstone's theorem in his Lectures on QFT
I am working through the proof of Goldstone's theorem in Coleman's Lectures on QFT in chapter 43.4.
He uses a Källén-Lehmann-like spectral representation of
$$\langle 0 | j_{\mu}\left(x\right)\phi\...
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Goldstone bosons in 2 and 3 quark flavor symmetries [closed]
In my (undergraduate) advanced elementary particles class last semester, we learnt that for a 2 quark (u/d) model the symmetry of the Lagrangian is (and breaks as)
$$
U(2)_L \otimes U(2)_R = SU(2)_L \...
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Explanation of massive Goldstone modes
I'm solving this exercise with a Heisenberg Hamiltonean in linear spin-wave theory and at some point we are asked to compute the dispersion relation at $k=0$, which leads me to finding two different ...
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Global symmetries QCD goldstone bosons
Beside the local $SU(3)$-Color-symmetrie The QCD Lagrangian also has global symmetries:
$$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} $$
$SU(...
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liquid-vapor interface goldstone modes
The free energy of a liquid-vapor interface (far from critical point) can be approximates as
$$
\mathcal{F}=γ A+\frac{γ}{2}\int dxdy|\nabla h(x,y)|^2
$$
where $h(x,y)$ is the height of the interface ...
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What is meant by the statement that Wigner-Weyl is linear realization and Nambu Goldstone is nonlinear realization?
In a paper, "Nonlinear Realization of Global Symmetries" by Zhong-Zhi Xianyu, I see the line
"There are basically two ways of symmetry realization in Hilbert space. One is such that ...
