I detail three major mathematical developments that led to the emergence of Yang-Mills theories as the foundation for the standard model of particle physics. In less than ten years, work on renormalizability, the renormalization group, and lattice quantum field theory highlighted the utility of Yang-Mills type models of quantum field theory by connecting poorly understood candidate dynamical models to emerging experimental results.The model was the result of developments in mathematical physics from 1960-1975. The paper describes these pretty well.
As the paper explains, renormalizing gauge theories was the crucial development.
The story ends in about 1975, with a satisfactory theory of all four fundamental forces, and agreement with experiment for the foreseeable future. So did physicists celebrate solving all their big problems? No. They embarked on string theory and billion-dollar searches for SUSY particles. None of this has amounted to anything.
Historians will record a golden age of theoretical physics that ran from Maxwell in about 1860 to the standard model in 1975.
Ah, the Standard Model...a model so complete it only has no accounting whatsoever of gravity, mass, time, or inertia...in other words, it can't actually do physics involving anything that moves...which seems to be most of the observable universe.ReplyDelete
Just a few loose ends to be tidied up, and them I'm sure we will know everything. /s
Renormalization is where things seriously went wrong, it's what happens when you pretend you can get agreement with observation by truncating your equation's infinities into finite quantities because... you waved your hands very vigorously and spoke convincingly, and have been getting away with it for decades...according to Richard Feynman.
"The shell game that we play to find n and j is technically called renormalization. But no matter how clever the word, it is what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving the theory of quantum electrodynamics is mathematically self-consistent. .... I suspect that renormalization is not mathematically legitimate."