QCD & SU(3): Explaining Particle Transformations

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SUMMARY

Quantum Chromodynamics (QCD) explains particle transformations under the SU(3) group, specifically regarding color charge. All particles possess defined transformation properties under SU(3)_color; quarks transform under the fundamental representation while leptons are invariant, belonging to the trivial singlet representation. Observed hadrons are also color singlets, illustrating the concept of confinement. While the explanation of confinement can be intuitive, it lacks a rigorous mathematical proof.

PREREQUISITES
  • Understanding of Quantum Chromodynamics (QCD)
  • Familiarity with group theory, specifically SU(3) transformations
  • Knowledge of particle physics, particularly quarks and leptons
  • Basic concepts of confinement in quantum field theory
NEXT STEPS
  • Read D. Griffiths' "Introduction to Elementary Particles" for foundational knowledge
  • Study the mathematical framework of SU(3) group theory
  • Explore advanced topics in confinement and its implications in particle physics
  • Investigate the role of color charge in QCD and its effects on particle interactions
USEFUL FOR

Students and researchers in particle physics, theoretical physicists, and anyone interested in the mathematical foundations of QCD and particle transformations.

jinbaw
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Can you please specify a reference to help me understand how QCD explains the fact that all particles observed in nature transforms under SU(3).
 
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Not all particles transform under SU(3).

If searching around on wikipedia is insufficient for you, I'd suggest picking up an undergrad text on particle physics. D. Griffiths, "Introduction to Elementary Particles," is a particularly good one.
 
okay, thanks
 
Actually the statement "not all particles transform under SU(3)" could be misleading. All particles have a well-defined transformation property under SU(3)_color. Quarks for instance transform under the fundamental representation. Leptons belong to the trivial singlet representation, the identity, they are invariant under SU(3)_color rotations. Observed hadrons also are color singlet, this is essentially confinement. We can understand this property by hand-waving, but there is no definite mathematical, rigorous, proof of confinement.
 

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