Singlets and Doublets in SU(2)

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SUMMARY

The discussion focuses on the properties of singlets and doublets in the context of SU(2) symmetry. It establishes that the product of two singlets does not break SU(2) symmetry, while the product of two singlets and a doublet does break this symmetry. The key takeaway is that any non-singlet with a non-zero expectation value in the vacuum state of the theory results in the breaking of SU(2) symmetry.

PREREQUISITES
  • Understanding of SU(2) symmetry in particle physics
  • Familiarity with the concepts of singlets and doublets
  • Knowledge of vacuum expectation values in quantum field theory
  • Basic principles of representation theory in physics
NEXT STEPS
  • Research the implications of symmetry breaking in SU(2) theories
  • Study the role of vacuum expectation values in quantum field theory
  • Explore representation theory related to SU(2) and its applications
  • Examine examples of singlet and doublet representations in particle physics
USEFUL FOR

This discussion is beneficial for theoretical physicists, students of quantum field theory, and anyone interested in the implications of symmetry in particle physics, particularly within the framework of SU(2).

ryanwilk
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Hi, this is probably very simple.

1) What is the product of two singlets?
2) What is the product of two singlets and a doublet?

It looks like (2) breaks SU(2) symmetry and (1) doesn't, but I don't really understand why =/.

Any help would be appreciated,

Thanks!
 
Physics news on Phys.org
Any representation remains the same when taking a product of it and a singlet


1) A singlet

2) A doublet

any non singlet which has a non zero expectation value in the vacuum of the theory breaks the SU(2) symmetry.
 

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