  Weyl applied his work in group theory and his earlier work in  analysis and spectral theory to the new theory of quantum mechanics.  Weyl’s mathematical analysis of the foundations of quantum mechanics  showed that regularities in a physical theory are most fruitfully  understood in terms of symmetry groups. Weyl’s (1928) book  Gruppentheorie und Quantenmechanik (Group Theory and  Quantum Mechanics) deals not only with the theory of quantum  mechanics but also with relativistic quantum electrodynamics. In this work Weyl also presented a very early analysis of discrete symmetries which later stimulated Dirac to predict the existence of the positron and the antiproton.