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In the late 1920s, Eugene Wigner highlighted the role that group theory and representation theory play in the analysis of quantum mechanics, for instance in the analysis of atomic spectra?. While many applications of groups and their representations to quantum physics had more or less explicitly been observed before, Wigner stood out as making the mathematical formalism fully explicit. This attitude was not well received by some of his colleagues, who felt that this formal mathematics had no place in physics. In particular Erwin Schrödinger is said (Wigner (1981)) to have spoken of the Gruppenpest (German for “plague of group theory”) which ought to be abandoned.
Eventually this resistence vanished and turned into its opposite in theoretical fundamental physics: in the classification of fundamental particles by unitary representations of the Poincaré group introduced by Hermann Weyl, in the description of gauge theory in terms of associated bundles given by representations of gauge groups. Today almost the first thing that one wants to know about a physical theory is its gauge group and the representations of it that play a role.
A transcript of an interview with Wigner where he mentions Schrödinger’s remark on the Gruppenpest is here:
A historical anlysis of Wigner’s work on group theory with a remark on the Gruppenpest comment is in