Measurements and electroweak gauge invariance/transformations

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SUMMARY

The discussion focuses on the invariance of measurements under gauge transformations in the standard model, specifically addressing SU(2) rotations in electroweak theory. It highlights that while gauge transformations like SU(3) and U(1) do not result in measurable changes, SU(2) transformations can interchange quark flavors and leptons, such as electrons and neutrinos. The broken symmetry and the role of the Higgs field, particularly in the unitary gauge where the Higgs field acquires a vacuum expectation value (VeV), are crucial to understanding mass generation through the Higgs-Lepton Yukawa interaction. The conclusion emphasizes that transformed particles retain the properties of their original counterparts.

PREREQUISITES
  • Understanding of gauge invariance in quantum field theory
  • Familiarity with the Standard Model of particle physics
  • Knowledge of electroweak theory and symmetry breaking
  • Concept of Higgs field and vacuum expectation value (VeV)
NEXT STEPS
  • Study the implications of spontaneous symmetry breaking (SSB) in electroweak theory
  • Explore the role of the Higgs-Lepton Yukawa interaction in mass generation
  • Investigate the properties of SU(2) gauge transformations and their effects on particle interchangeability
  • Learn about the unitary gauge and its significance in particle physics
USEFUL FOR

Particle physicists, theoretical physicists, and students studying the Standard Model and electroweak interactions will benefit from this discussion.

Michael Price
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TL;DR
Gauge transforms have no effect on measurements, so how can an electroweak SU(2) rotation transform an electron into a neutrino and not be observed?
Most gauge transformations in the standard model are easy to see are measurement invariant. Coordinate transformations, SU(3) quark colours, U(1) phase rotations for charged particles all result in no measurable changes. But how does this work for SU(2) rotations in electroweak theory, where quarks flavours, and electrons and neutrinos, are interchangeable? My guess is that this involves the broken nature of the symmetry and the Higgs field. Is this correct?
 
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In the unitary gauge the Higgs field acquires a VeV only in one of its components and so only one component of the left-handed lepton doublet get a mass term from the Higgs-Lepton Yukawa interaction. So I suppose in arbitrary gauge, we can always diagnolize the mass term and the massive component just gets called an electron by convention.

I suppose you could SU(2) rotate the electron into the neutrino and vice versa even after SSB, but then the Higgs field and all the Gauge fields would all get transformed and the new "neutrino" you end up with will have all the same propeties as the electron.
 
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HomogenousCow said:
In the unitary gauge the Higgs field acquires a VeV only in one of its components and so only one component of the left-handed lepton doublet get a mass term from the Higgs-Lepton Yukawa interaction. So I suppose in arbitrary gauge, we can always diagnolize the mass term and the massive component just gets called an electron by convention.

I suppose you could SU(2) rotate the electron into the neutrino and vice versa even after SSB, but then the Higgs field and all the Gauge fields would all get transformed and the new "neutrino" you end up with will have all the same properties as the electron.
Thanks, that does indeed work. Whatever a particle gets transformed into has the properties of the original particle.
 

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