Editing Quantum field theory (section)

===Non-renormalizability===
Given the tremendous success of QED, many theorists believed, in the few years after 1949, that QFT could soon provide an understanding of all microscopic phenomena, not only the interactions between photons, electrons, and positrons. Contrary to this optimism, QFT entered yet another period of depression that lasted for almost two decades.{{r|weinberg|page1=30}}

The first obstacle was the limited applicability of the renormalization procedure. In perturbative calculations in QED, all infinite quantities could be eliminated by redefining a small (finite) number of physical quantities (namely the mass and charge of the electron). Dyson proved in 1949 that this is only possible for a small class of theories called "renormalizable theories", of which QED is an example. However, most theories, including the [[Fermi's interaction|Fermi theory]] of the [[weak interaction]], are "non-renormalizable". Any perturbative calculation in these theories beyond the first order would result in infinities that could not be removed by redefining a finite number of physical quantities.{{r|weinberg|page1=30}}

The second major problem stemmed from the limited validity of the Feynman diagram method, which is based on a series expansion in perturbation theory. In order for the series to converge and low-order calculations to be a good approximation, the [[coupling constant]], in which the series is expanded, must be a sufficiently small number. The coupling constant in QED is the [[fine-structure constant]] {{math|''α'' ≈ 1/137}}, which is small enough that only the simplest, lowest order, Feynman diagrams need to be considered in realistic calculations. In contrast, the coupling constant in the [[strong interaction]] is roughly of the order of one, making complicated, higher order, Feynman diagrams just as important as simple ones. There was thus no way of deriving reliable quantitative predictions for the strong interaction using perturbative QFT methods.{{r|weinberg|page1=31}}

With these difficulties looming, many theorists began to turn away from QFT. Some focused on [[symmetry (physics)|symmetry]] principles and [[conservation law]]s, while others picked up the old S-matrix theory of Wheeler and Heisenberg. QFT was used heuristically as guiding principles, but not as a basis for quantitative calculations.{{r|weinberg|page1=31}}