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 modes/momentum generation from the vacuum
I'm quite confused by two short paragraphs in Schwarz 28. He proves that $$ Q = \int d^3 x J_0(x) = \int d^3 x \sum_m \frac{\partial L}{\partial \dot \phi_m} \frac{\delta \phi_m}{\delta \alpha} \tag{...
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Goldstone boson in Higgs Mechanism
On P&S's QFT book, page 693, the book discussed "Systematics of the Higgs Mechanism". For the kinetic part of Lagrangian,
$$ \frac{1}{2}\left(D_\mu \phi_i\right)^2=\frac{1}{2}\left(\...
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Goldstone Bosons and Criticality
In the presence of spontaneous symmetry breaking of a continuous symmetry, there are massless goldstone bosons. However, they are not treated in the discussions of critical phenomena. Naively I would ...
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How to construct Goldstone bosons from a conserved charge?
The Goldstone boson associated with a conserved charge is described by
$$
|\pi(\vec p)\rangle\propto \int d^3x~e^{i\vec p\cdot\vec x}j_0(x)|0\rangle.
$$
How can I see that this is a state with energy ...
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Why magnon band is half filled in XY model?
This is my first contact with that field so I hope that I describe my problem clearly.
In the notes I follow we consider a 1-dimensional XXZ problem with
\begin{equation}
\hat{H}_{XXZ}=-J_{\perp}\sum_{...
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Spontaneous Symmetry Breaking / Explicit Symmetry Breaking [closed]
I'm trying to understand the SSB and explicit symmetry breaking.
If we have a complex scalar field theory with Mexican hat potential,
$$\phi(x)=\frac{\sigma(x)}{\sqrt{2}}e^{i\Pi(x)/v}$$
choice of the ...
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Quantum numbers of a symmetry generator?
I am trying to understand the italicized part: a broken symmetry leads to a massless Goldstone boson with same quantum numbers as broken symmetry generator. Weinberg talks about it in Chapter 19, if ...
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Axions as goldstone bosons of anomalous $U(1)$ symmetry
In the $m_q \rightarrow 0$ limit the QCD lagrangian has the symmetry $U(N)_V \times U(N)_A$. Including just the two lightest quarks, $N=2$, and looking at the $U(2)_A=SU(2)_A \times U(1)_A$ part, we ...
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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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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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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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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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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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Identification of physical pion states in chiral perturbation theory
In chiral perturbation theory, we introduce the parametrization of the Goldstone manifold
$$
U = \exp\left( i \frac{1}{f_\pi} \pi_a \sigma_a\right),
$$
where $\sigma_a$ are the Pauli matrices. Most ...
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Goldstone and longitudinal polarization equivalence between off-shell $W$s
If I understand correctly, the couplings of the longitudinal component of the $W$ and $Z$ bosons should be "equivalent" to the Goldstone bosons they ate after SSB.
In practice, this makes ...
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