How can we unify electromagnetic force U(1) and weak force SU(2)?

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SUMMARY

The unification of electromagnetic force U(1) and weak force SU(2) is achieved through the spontaneous symmetry breaking of SU(2) by the Higgs field, resulting in the electroweak interaction symmetry of U(1) x SU(2). The U(1) weak hypercharge and SU(2) weak isospin are entangled, but the broken SU(2) symmetry leads to a residual U(1) electromagnetic symmetry, which is responsible for the massless photon. This process involves a U(1) rotation characterized by the Weinberg angle, which mixes weak hypercharge with the weak isospin components.

PREREQUISITES
  • Understanding of SU(2) symmetry and its role in particle physics
  • Familiarity with U(1) gauge theories and their implications
  • Knowledge of the Higgs mechanism and spontaneous symmetry breaking
  • Basic concepts of the Glashow-Weinberg-Salam model
NEXT STEPS
  • Study the Higgs mechanism in detail, focusing on its role in symmetry breaking
  • Explore the Glashow-Weinberg-Salam model for a comprehensive understanding of electroweak unification
  • Learn about the Weinberg angle and its significance in particle interactions
  • Investigate the implications of U(1) and SU(2) symmetries in modern physics
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Physicists, students of theoretical physics, and anyone interested in the unification of fundamental forces and the Standard Model of particle physics.

ndung200790
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Please teach me this:
How can we unify electromagnetic and weak interactions?Is it correct that the SU(2) symmetry(flavor symmetry of fermions) is spontaniously broken(by Higgs Field) and the symmetry(be broken) ''become'' U(1)xSU(2) symmetry that is the symmetry of electroweak interaction?
Thank you very much for your kind helping.
 
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It's bit more complicated.

One entangles U(1)weak hypercharge * SU(2)weak isospin, but the SU(2) symmetry which is broken - and therefore the residual U(1)el.-mag. symmetry which survives and gives us the massless photon - are different ones. The reason is that one applies an U(1) rotation involving the so-called Weinberg angle. This rotation mixes weak hypercharge and the 3-component of the weak isospin.

Have a look at http://en.wikipedia.org/wiki/Glashow-Weinberg-Salam_model
 

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