What is a non-Abelian gauge theory?

A non-Abelian gauge theory is a type of field theory where the Lagrangian remains invariant under local symmetry transformations that form a non-commutative Lie group. Because the symmetry group is non-commutative, these theories typically involve interacting gauge fields, with Yang–Mills theory serving as the classic example. They form the mathematical backbone of the Standard Model, describing both the strong and electroweak interactions of elementary particles.

What we know

• If the symmetry group of a gauge theory is non-commutative, the theory is referred to as a non-Abelian gauge theory. [2]
• The usual example of a non-Abelian gauge theory is the Yang–Mills theory. [2]
• The Standard Model is a non-Abelian gauge theory with the symmetry group U(1) × SU(2) × SU(3). [2, 3]
• Yang–Mills theory is based on a special unitary group SU(n) or another compact Lie group. [3]

Where to go next

• a case in pointWhat is Yang-Mills theory?
• compared withHow does Quantum Electrodynamics differ as an Abelian gauge theory?
• the bigger pictureWhat is the Standard Model of particle physics?
• whoWho developed Yang-Mills theory?
• how it workedWhat is a quantum field theory?
• an unexpected connectionHow do gauge theories explain general relativity and gravitation?Gauge theories are not just for subatomic particles; they are also important in explaining gravitation in the theory of general relativity through tensor fields and alternative gravity formulations.

Sources

• [1]gauge theory (Wikidata Q214850) · CC0 1.0
• [2]Gauge theory · CC BY-SA 4.0
• [3]Yang–Mills theory · CC BY-SA 4.0
• [4]Non-abelian · CC BY-SA 4.0
• [5]Quantum field theory · CC BY-SA 4.0

Your path

1. What role does the forest floor play in biogeochemical cycles?
2. /What is Papyrus Fouad 266?
3. /What is a non-Abelian gauge theory?