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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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 ...
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Nambu-Goldstone mode without symmetry breaking
Superfluidity is often explained in terms of spontaneous breaking of global $U(1)$ symmetry. However, we know that in real, finite-size quantum systems, this symmetry can never be broken. Quantum ...
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Property of representations of Lie Groups in Weinberg's Quantum Theory of Fields
In section 19.6, page 212-213 in Weinberg's Quantum Theory of Fields Volume II, Weinberg shows that on can always eliminate the Goldstone Bosons from a field $\psi(x)$, by use of a space-dependent ...
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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 ...
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SSB of Spacetime Symmetries in 2d
Colemans theorem states that there are no Goldstone Bosons in $d=2$ spacetime dimensions : https://inspirehep.net/literature/83738 because there is no spontaneous symmetry breaking.
However I have ...
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Spontaneous symmetry breaking in the Standard Model. What is "broken"?
I know this question has been asked other times, but I am looking for a confirmation of the following.
When we say that the gauge group of the standard model is $G_{SM} = SU(3)_{c} \times SU(2)_{L} \...
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Spontaneous Chiral Symmetry Breaking in Schwartz
I am reading M. Schwartz's book on QFT, equation (28.24)/(28.22). They say that a set scalar fields will transform as, where $g_L$ belongs to $SU(2)_{L}$ and $g_R$ belongs to $SU(2)_R$:
$$\Sigma\...
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Why is that if the broken symmetry is realized linearly we can not find rationale for the Lagrangian of the sigma model?
In the book The Quantum theory of fields Vol. 2 at page 193 Weinberg says
$$
\mathscr{L}=-\frac{1}{2} \partial_{\mu} \phi_{n} \partial^{\mu} \phi_{n}-\frac{\mathscr{M}^{2}}{2} \phi_{n} \phi_{n}-\...
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What does the absence of these Goldstone boson interactions mean physically?
I have read that in several statistical models exhibiting spontaneous symmetry breaking, the resulting Goldstone bosons do not interact with each other via $\theta^{2n}$ terms — only via derivative ...
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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 ...
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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 ...
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How scalars appear in Goldstone's theorem
Let $G$ be a lie group and $G_i$ its generators. Suppose for a set of fields $\chi_{\alpha}(x)$ we have
$$
\left[G_{i}, \chi_{\alpha}(x)\right]=-\left(g_{i}\right)_{\alpha \beta} \chi_{\beta}(x)
$$
If ...
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Fetter and Walecka's derivation of Goldstone's Theorem
I've been learning Green's Functions (Zero-Temprature) from Fetter and Walecka's Quantum Theory of Many-Particle Systems, and find it hard to understand the proof of Goldstone's Theorem, in page 111, ...
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Question about the Weinberg proof of the Goldstone's theorem
When proving Goldstone's theorem in Vol. 2, p. 171, Weinberg takes the following:
$$\langle \{J^\lambda(y),\phi_n(x)\}\rangle= \frac{\partial}{\partial y_\lambda}\int d\mu^2 \rho_n(\mu^2) \left[ \...
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Can be Goldstone bosons measured?
I'm reading about the Higgs mechanism considering the Lagrangian:
$$
\mathcal{L}=-\frac{1}{4}F^{\mu\nu}F_{\mu\nu} + \left(D_\mu\phi\right)\left(D^\mu\phi\right)^\dagger-\mu^2\left(\phi\phi\right)^\...
