QCD & SU(3): Explaining Particle Transformations

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Discussion Overview

The discussion centers on the transformation properties of particles under the SU(3) group in the context of Quantum Chromodynamics (QCD). Participants explore the implications of these transformations for different types of particles, including quarks and leptons, and the concept of confinement.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant requests references to understand how QCD explains particle transformations under SU(3).
  • Another participant asserts that not all particles transform under SU(3), suggesting further reading in undergraduate texts on particle physics.
  • A later reply clarifies that while all particles have transformation properties under SU(3)_color, quarks transform under the fundamental representation, whereas leptons are invariant under SU(3)_color rotations, belonging to the trivial singlet representation.
  • This reply also notes that observed hadrons are color singlets, linking this to the concept of confinement, but emphasizes the lack of a rigorous mathematical proof for confinement.

Areas of Agreement / Disagreement

Participants express disagreement regarding the transformation properties of particles under SU(3), with differing interpretations of which particles are included and how they transform.

Contextual Notes

The discussion highlights potential ambiguities in the definitions of particle classifications and transformation properties, as well as the unresolved nature of mathematical proofs related to confinement in QCD.

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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