Yang-Mills Theory Explained: SU(N) Symmetry & Gauge Theory

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Discussion Overview

The discussion revolves around the concept of Yang-Mills Theory, particularly its relationship with SU(N) symmetry and its application as a gauge theory. Participants explore the generality of the theory and its specific instances, such as ElectroWeak and Chromodynamics, while also considering alternative gauge groups.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants inquire whether Yang-Mills Theory is a general theory based on SU(N) symmetry applicable to specific cases like ElectroWeak and Chromodynamics.
  • One participant affirms that Yang-Mills Theory is indeed a gauge theory, referencing external sources for further information.
  • Another participant suggests that Yang-Mills Theory is not limited to SU(N) and can also involve other groups such as SO(N) and Sp(N), emphasizing the need for gauge fields to maintain gauge invariance.
  • A later reply asserts that the gauge group must be nonabelian for the theory to differ from quantum electrodynamics.

Areas of Agreement / Disagreement

Participants express differing views on the applicability and scope of Yang-Mills Theory, with no consensus reached regarding the specific nature of the gauge groups involved.

Contextual Notes

There are unresolved aspects regarding the definitions and implications of gauge invariance and the characteristics of nonabelian gauge groups.

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What exactly is a Yang-Mills Theory? Is it a general theory, based on SU(N) symmetry, which can then be applied for particular cases (ElectroWeak, Chromodynamics) ? Is it like a general mathematical model of gauge theory ?
 
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Qubix said:
What exactly is a Yang-Mills Theory? Is it a general theory, based on SU(N) symmetry, which can then be applied for particular cases (ElectroWeak, Chromodynamics) ? Is it like a general mathematical model of gauge theory ?

Yes its a gauge theory:

http://en.wikipedia.org/wiki/Yang-Mills_theory
 
Not necessarily SU(N). It can also be like SO(N), Sp(N), etc. The idea is we need to introduce gauge fields to keep the theory gauge invariant.
 
The gauge group of the field theory needs to be nonabelian, else it would just be quantum electrodynamics.
 

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