I try to explain the significance of group theory in physics, from a non-particle physicist’s standpoint.
Many physicist seem to forget that the Lie algebra is not the whole deal in specifying a Lie group. I explain the correspondence between Lie groups and algebras in more detail.
All Lie groups have an adjoint representation. Indeed the adjoint representation is what truly gives meaning to the Jacobi identity.
Nearly one hundred years after Hermann Weyl first proposed looking for new theories by postulating their invariance with respect to symmetries (his postulated “Eichinvarianz” to try to unify electromagnetism and general relativity), modern particle physics sees gauge symmetry as a keystone. Somehow this all seemed highly contrived to me. Why is this principle so important?