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Details theoretical disposition of Nmbu-goldstone bosons eating gauge bosons inthe liht of spontaneous Symmety Breaking.
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Certainly! Let’s delve into the fascinating realm of spontaneous symmetry breaking and the intriguing concept of Nambu-Goldstone bosons.
Spontaneous Symmetry Breaking (SSB): Spontaneous symmetry breaking is a phenomenon that occurs in many-body systems, where the stable solutions of dynamical equations exhibit less symmetry than the equations themselves. Here are some key points:
Ordinary Crystals and Ferromagnets:
Ordinary crystals break translation symmetry down to a discrete subgroup, while ferromagnets break rotational symmetry.
In both cases, the stable configurations have less symmetry than the underlying equations governing the system.
Superfluids and Superconductors:
Superfluids (like liquid helium-4 at low temperatures) and superconductors (such as certain metals at low temperatures) also exhibit spontaneous symmetry breaking.
In superfluids, the broken symmetry is associated with the U(1) phase symmetry related to the conservation of helium-4 atom number.
In superconductors, the broken symmetry is a local (gauged) symmetry associated with electron number, which photons respond to.
Chiral Symmetry in QCD:
The approximate chiral symmetry SUL(2) × SU(2)R of Quantum Chromodynamics (QCD) is an example of spontaneous symmetry breaking.
This symmetry involves independent unitary transformations among left-handed (uL, dL) and right-handed (uR, dR) helicity states.
Although not exact within QCD due to the small masses of u and d quarks, the symmetry breaking SU(2)L × SU(2)R → SU(2)L+R is predominantly spontaneous.
Pions, which are Nambu-Goldstone bosons, emerge from this broken symmetry and play a crucial role in low-energy interactions.
Electroweak Symmetry Breaking:
The electroweak theory postulates the gauge symmetry SU(2) × U(1).
To avoid massless gauge bosons (which unbroken gauge symmetry would imply), we break the symmetry spontaneously.
The mechanism here is similar to superconductivity: the three would-be Goldstone bosons associated with the broken generators are “eaten” by the three gauge bosons (W+, W-, Z) to give them mass.
This process ensures that the weak force carriers acquire mass while preserving gauge symmetry.
In summary, Nambu-Goldstone bosons arise from spontaneous symmetry breaking, and their behavior is intimately connected to the fundamental forces and particles in our universe12. If you’d like to explore this topic further or have any specific questions, feel free to ask! 🌟
Learn more
1
web.mit.edu
2
en.wikipedia.org
3
scientificlib.com
4
physics.stackexchange.com
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