The electromagnetic force governs light and electric currents, while the weak interaction drives radioactive beta decay. In the 1960s a gauge-theory framework called electroweak theory tried to unify them, but early quantum calculations produced infinities that threatened the theory. ’t Hooft and Veltman refined the method of renormalization and proved the theory yields finite, sensible results. They also created computer programs that automated the cumbersome calculations and predicted quantities such as the masses of the W and Z bosons. Later accelerator experiments confirmed these predictions, making electroweak theory a cornerstone of the Standard Model. The Standard Model guides today’s particle research and underlies technologies like PET medical imaging and semiconductor inspection. Their achievement thus built a strong bridge between fundamental science and everyday applications.

Electroweak theory, based on the SU(2)L×U(1)Y gauge symmetry and the Higgs mechanism, accounts for massive W and Z bosons and the massless photon within one framework. Yet it was unclear whether a non-Abelian gauge theory with spontaneous symmetry breaking could remain consistent at the quantum level. ’t Hooft employed BRST symmetry and Faddeev–Popov ghosts to prove rigorously that all ultraviolet divergences can be absorbed into a finite set of physical parameters, establishing renormalizability. Together with Veltman he refined dimensional regularization and developed FORTRAN codes that automatically handled hundreds of thousands of loop terms. As a result the theory preserved S-matrix unitarity and gained predictive power. Their techniques were later extended to quantum chromodynamics and supersymmetric models, enabling indirect determinations of the top-quark and Higgs masses from precision electroweak data. The design goals of LEP, Tevatron, and the LHC relied heavily on their estimates of theoretical uncertainties. The generalized Ward–Takahashi identities ensuring gauge-fixing independence are embedded in modern automated tools such as FeynArts and MadGraph. When the Standard Model is linked to cosmology or neutrino physics, their mathematical framework provides the basis for reliable error control.

Starting with tests in the λφ4 model, ’t Hooft demonstrated the renormalizability of non-Abelian gauge theories in Rξ gauges and guaranteed covariant quantum gauge invariance through BRST cohomology. His derivation of the Slavnov–Taylor identities established that gauge-fixing parameters do not affect physical observables, thereby securing S-matrix unitarity. Veltman, using the Schoonschip algebra system developed during his stay in Spain, devised the Passarino–Veltman reduction that converts tensor integrals into scalar ones, greatly streamlining multi-loop computations. The duo adopted dimensional regularization, addressed γ5 treatment and axial anomalies, and completed the consistent construction of the Standard Model. Their framework became the industry standard for automatic computation suites and for NLO/NNLO corrections, forming the backbone of the Δr analysis in the GF, α, MZ input schemes of precision electroweak studies. Global fits of the 96-point LEP EWWG dataset and the LHC’s EWK-NNLO packages reference their formalism directly in code. Today, higher-order logarithmic resummations and effective-field-theory matchings in hadron-collision experiments routinely default to the ’t Hooft–Veltman scheme.