4 ms·
Only if you take U(1) as your gauge group. If you pick a non-abelian group the equations are not linear and solutions are not superposable.
by evanb 6y ago
Only if you take U(1) as your gauge group. If you pick a non-abelian group the equations are not linear and solutions are not superposable.
- mrfox321 6y agoMaxwell's equations are linear. The nonlinearity of quantum field theory is not relevant here.
- evanb 6y agoI was trying to convey that "Maxwell's equations" can name not just the equations that describe electromagnetism, which has a U(1) gauge group, but can name an entire category of gauge theory equations---one for each gauge group. If the gauge group isn't abelian Maxwell's equations are _not_ linear.
- a1369209993 6y agoCan you give a example of a set of gauge theory equations for a non-U(1) gauge group? This seems interesting but I'm not really sure what it would actually look like.
- evanb 6y agoQCD is a nonabelian gauge theory, for example. The generalized Maxwell action is called the Yang-Mills action. The corresponding equations are very similar, except the gauge-covariant derivatives do not take a particularly simple form (which they do in the U(1) case because U(1) is abelian). https://physicstravelguide.com/equations/yang_mills_equations#tab__why_is_it_interesting https://physicstravelguide.com/equations/yang_mills_equation...