nLab
Yang-Mills theory

Idea

Yang–Mills theory is a gauge theory on 4-dimensional (pseudo)Riemannian manifold $X$ whose field is the Yang–Mills field – a cocycle $\hat{F} \in H (X, \bar{B} U (n))$ in differential nonabelian cohomology represented by a vector bundle with connection – and whose action functional is

\hat{F} \mapsto \int_{X} F \land ⋆ F + θ \int_{X} F \land F

for

$F$ the field strength, $𝔲 (n)$ -valued differential 2-form on $X$ ( with $𝔲 (n)$ the Lie algebra of the unitary group $U (n)$ );
$⋆$ the Hodge star operator;
$θ$ some real number.

All gauge fields in the standard model of particle physics as well as in GUT models are Yang–Mills fields.

The matter fields in the standard model are spinors charged under the Yang-Mills field. See

Revised on May 28, 2010 15:32:10 by Urs Schreiber (131.211.36.96)