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Maxwell's equations are linear. The nonlinearity of quantum field theory is not relevant here.
by mrfox321 6y ago
Maxwell'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...