A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. ...
What is the precise definition of unification of fields (in classical and quantum mechanics)? In general, does unification of a field mean that we can write both of them at both sides of an equation ...