How does non-abelian gauge symmetry affect quark interactions?

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Discussion Overview

The discussion centers on the implications of non-abelian gauge symmetry, particularly in relation to quark interactions and the phenomenon of asymptotic freedom in quantum chromodynamics (QCD). It explores theoretical aspects and the behavior of coupling constants under varying conditions.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how non-abelian gauge symmetry contributes to asymptotic freedom for quarks.
  • Another participant explains that in non-Abelian gauge theories, gauge fields carry charge, leading to self-interactions that affect the coupling constant, which decreases with increasing energy in QCD, influenced by the number of colors and flavors.
  • A participant inquires about the non-commutative nature of the color field.
  • It is noted that the gauge group for QCD is SU(3), contrasting it with the abelian gauge group of quantum electrodynamics (QED), which is U(1).

Areas of Agreement / Disagreement

Participants present various viewpoints on the effects of non-abelian gauge symmetry, with some aspects being clarified while other questions remain unresolved, indicating that multiple competing views exist.

Contextual Notes

There are limitations regarding the dependence on the number of colors and flavors in the discussion of coupling constants, as well as the implications of non-commutativity in the color field, which are not fully explored.

Who May Find This Useful

This discussion may be of interest to those studying quantum field theory, particularly in the context of gauge theories and their implications for particle interactions.

kurious
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How does a non-abelian gauge symmetry lead to
asymptotic freedom for quarks?
 
Physics news on Phys.org
In a non-Abelian gauge theory, the gauge fields also carry the charge. (I'm sure you've been told before that gluons carry color). The self-interaction of the gauge fields is non-trivial, but in the case of QCD they cause a decrease in the coupling constant with increasing energy. In fact, the actual behavior depends on the number of colors and flavors - more colors favor decreasing coupling and more flavors favor increasing coupling. With 3 colors and 6 flavors, the result is decreasing.
 
In what respect is the colour field non-commutative?
 
The gauge group is SU(3) which is non-abelian. The gauge group of QED is simply the unit circle U(1) which is abelian (the phases add in the unit cirlce).
 

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