Two of the most profound scientific discoveries of the early twentieth century were special relativity and quantum mechanics. With special (and general) relativity came the notion that physics should be local. Interactions should be carried by dynamical fields in space-time. Quantum mechanics altered the questions which physicists asked about phenomena; the rules governing microscopic (and some macroscopic) phenomena were not those of classical mechanics. When these ideas are combined, they take on their full force, in the form of quantum field theory. Particles themselves are localized, finite-energy excitations of fields. Otherwise mysterious phenomena such as the connection of spin and statistics are immediate consequences of this marriage. But quantum field theory does pose a serious challenge. The Schrödinger equation seems to single out time, making a manifestly relativistic description difficult. More serious, but closely related, the number of degrees of freedom is infinite. In the 1920s and 1930s, physicists performed conventional perturbation theory calculations in the quantum theory of electrodynamics, quantum electrodynamics or QED, and obtained expressions which were neither Lorentz invariant nor finite. Until the late 1940s, these problems stymied any quantitative progress, and there was serious doubt whether quantum field theory was a sensible framework for physics.

Despite these concerns, quantum field theory proved a valuable tool with which to consider problems of fundamental interactions. Yukawa proposed a field theory of the nuclear force, in which the basic quanta were mesons. The corresponding particle was discovered shortly after the Second World War. Fermi was aware of Yukawa's theory, and proposed that the weak interactions arose through the exchange of some massive particle – essentially the W± bosons which were finally discovered in the 1980s.