In a series of papers written between 1926 and 1927, Eugene Wigner was the first to employ group-theoretical considerations to interpret the selection rules of atomic spectroscopy. He accomplished this by invoking the transformation properties of energy eigenstates with respect to operations which leave the system as a whole invariant (space rotations, mirror inversions, permutations of the electrons). Within a short time, this approach was successfully extended to include molecular and nuclear spectroscopy. Today, Wigner's results are taken for granted to the extent that it is difficult to see in the quantum numbers of Bohr, Sommerfeld or Landè something other than labels of the rotation group's representations.
While the historical significance of Wigner's work is widely recognized, it is nonetheless mostly regarded as a mere application of already existing mathematical tools to the analysis of problems that had already been solved by other means: a purely mathematical development with no impact on the physical interpretation of quantum theories. Contrary to this view, the working hypothesis of the present research project is that the encounter between group theory and and the old-quantum-theoretical notion of "selection rules" had a profound and long lasting impact on the physical content of quantum theory.
As noted by the historian Paul Forman, the interpretation of spectroscopic evidence in terms of stationary states and selection rules had been a very important conceptual model for spectroscopists working within the framework of the old quantum theory. The connection between selection rules and group theory allowed physicists to exprot this model into the new quantum mechanics. Within the new quantum-mechanical environment, the connection between selection rules and group theory contributed to creating a new type of symmetry arguments in which selection rules, rather than conservation laws, were regarded as the observable signature of an underlying physical symmetry. Interpreting experimental data in terms of selection rules, therefore, led to a redefinition of traditional conserved quantitites, notably of angular momentum. Once more, it was Wigner who, in a short paper published in 1928, drew attention to the new, quantum form of conservation laws, articulating what is today referred to as the quantum version of Noether's theorem.
The union between symmetry and selection rules was fruitful not only in the fields of atomic, molecular and nuclear spectroscopy. In the late 1940's, group theory - the Gruppenpest, as it had been disparagingly referred to in the 1930's - had to be resurrected to serve as a basis for of a new type of spectroscopy, one which attempted to create order among particles detected in cosmic rays. Here, too, Wigner played a prominent role, in particular with his paper on unitary representations of the inhomogeneous Lorentz group. by tracing these and other examples, this project aims at shifting our historical understanding of group theory from a mathematical sidelight to a central working tool.