How did 't Hooft prove gauge theories are renormalizable?
I proved renormalizability by developing a gauge-fixing procedure that preserves the symmetries of the theory at the quantum level. The key was to use dimensional regularization and the 't Hooft-Veltman scheme, which handles chiral anomalies carefully. I introduced the concept of the 't Hooft parameter, a mass scale that absorbs infinities, and showed that all divergences can be canceled by redefining a finite number of coupling constants and masses. Let us consider a simple example: in non-Abelian gauge theories, the ghost fields—fictitious particles that cancel unphysical polarizations—are essential. I demonstrated that the Slavnov-Taylor identities, which enforce gauge invariance, hold to all orders. This was not a trivial calculation; it required careful bookkeeping of Feynman diagrams. The result was that the electroweak theory became a predictive, finite framework, which later experiments at CERN confirmed with stunning precision.
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