Editing Color charge (section)

== Coupling constant and charge ==
In a [[quantum field theory]], a [[coupling constant]] and a charge are different but related notions. The coupling constant sets the magnitude of the force of interaction; for example, in [[quantum electrodynamics]], the [[fine-structure constant]] is a coupling constant. The charge in a [[gauge theory]] has to do with the way a particle transforms under the gauge symmetry; i.e., its [[group representation|representation]] under the gauge group. For example, the [[electron]] has charge −1 and the [[positron]] has charge +1, implying that the gauge transformation has opposite effects on them in some sense. Specifically, if a local [[gauge transformation]] {{math|''ϕ''(''x'')}} is applied in electrodynamics, then one finds (using [[tensor index notation]]):<math display="block">\begin{align}
A_\mu &\to A_\mu + \partial_\mu\,\phi(x) \\
\psi &\to \exp\left[+i\,Q\phi(x)\right]\; \psi \\
\bar\psi &\to \exp\left[-i\,Q\phi(x)\right] \; \bar\psi ~,
\end{align}</math>
where <math>A_\mu</math> is the [[photon]] field, and {{math|''ψ''}} is the electron field with {{math|1=''Q'' = −1}} (a bar over {{mvar|ψ}} denotes its antiparticle&nbsp;– the positron). Since QCD is a [[non-abelian group|non-abelian]] theory, the representations, and hence the color charges, are more complicated. They are dealt with in the next section.