Martinus (“Tini”) Veltman started his scientiﬁc career relatively late: he obtained his PhD from the University of Utrecht in 1963^{(1)} under the supervision of Leon Van Hove, but had already moved to CERN in 1961, where Van Hove had been named Leader of the CERN Theory Division. At CERN, Van Hove studied mainly hadronic physics but Veltman became interested in weak interactions^{(2)} and current algebras. It is in these ﬁelds that he made his most important and lasting contributions.

In around 1966, he was trying to understand the deeper origin of the conservation, or near conservation, of the weak currents. In particular, he tried to throw some light on the general confusion that prevailed at the time concerning the so-called “Schwinger terms” in the commutators of two current components. While on a visit from CERN to Brookhaven, he wrote a paper in which he suggested a set of divergence equations which generalised the notion of the covariant derivative of quantum electrodynamics. This fundamental idea was taken up the following year and developed further by John Stewart Bell. At that time, people had postulated the existence of a pair of charged, massive vector W^{±} bosons as intermediaries of the weak interactions so, motivated by these divergence equations, Veltman decided to study their ﬁeld theory properties. The electrodynamics of such charged bosons had been formulated already by T.D. Lee and C.N. Yang in 1962. They had shown that electromagnetic gauge invariance allows expression of the vector boson’s charge e, magnetic moment µ and quadrupole moment Q in terms of only two parameters, e and κ, as µ = e(1 + κ)/2m_{W} and Q = −eκ/m_{W2}. The resulting theory is highly divergent but Veltman noticed that many divergences cancel for the value κ = 1. This is the value predicted by a theory in which W^{±} and the photon form a Yang-Mills triplet. For Veltman, this was a clear signal that the theory of weak and electromagnetic interactions must obey a Yang-Mills gauge invariance.

The study of a massive Yang-Mills ﬁeld theory turned out to be very complicated, both conceptually, since the correct Feynman rules were not known and practically, because the number of terms grew very fast. Veltman had to develop a computer program to handle them. He called it “Schoonschip” (“Clean ship” in Dutch) and it was the ﬁrst program of symbolic manipulations applied to theoretical high-energy physics. Schoonschip opened the way to the modern computer codes used to manipulate Feynman diagrams, which are responsible for the enormous progress made with the sophisticated calculations of the Standard Model processes that have been produced in the last decades.

The experience Veltman had acquired in his thesis, working with diagrams in which the particles in the intermediate lines were on their mass shells, the so-called “cutting rules”, was precious. He spent 1968 at Orsay near Paris, where he lectured on Yang-Mills and path integrals and, in 1969, he was joined in Utrecht by Gerard ’t Hooft, a graduate student with whom he shared the 1999 Nobel Prize. Their work was a real “tour de force”. They invented and developed many techniques that became standards in particle physics. The citation of the Nobel Prize reads “… for elucidating the quantum structure of electroweak interactions in physics”. The importance of this work cannot be overestimated. Although the citation refers to the electroweak interactions, their result made possible the subsequent discovery of QCD. Since that time, gauge theories have become the universal language of fundamental physics.

Veltman and ’t Hooft gave the ﬁrst detailed presentation of their results at a small meeting in Orsay in 1971. This meeting was remarkable in many respects. Firstly, it oﬀered the ﬁrst complete picture of the renormalisation properties of Yang-Mills theories. Secondly, it triggered stimulating discussions among the participants, in particular regarding the vital importance of the axial current anomaly cancellation.

With the rise of the Standard Model, a long series of meetings was launched, which became known as “triangular meetings” (Paris-Rome-Utrecht). Subsequently extended to other European centres, the triangular meetings played an important role in the development of new ideas in ﬁeld theory and in establishing a European network in theoretical physics. Veltman was a central ﬁgure in those meetings.

After the discovery of the Intermediate Vector Bosons, several groups embarked on a systematic study of the higher order electroweak corrections to the predictions of the Standard Model. The group led by Veltman was among the most active. A particular focus of attention was the so-called ρ = M_{W} / cos θM_{Z} parameter. Veltman observed that its deviation from unity, the value predicted to lowest order in the Glashow-Weinberg-Salam theory, depends quadratically on the top quark mass and logarithmically on the Brout-Englert-Higgs boson mass. Precise determinations of the ρ parameter led eventually to a prediction of the top quark mass, conﬁrmed by the top quark discovery of CDF and DØ at Fermilab. Even more precise values of M_{W} and M_{top} led to signiﬁcant limitations on the BEH boson mass, in agreement with the mass of the scalar particle discovered by ATLAS and CMS in 2012.

Veltman stayed in Utrecht until 1981. He attracted many talented young students and established a very active school of theoretical high-energy physics in the Netherlands. He was a lifelong supporter of CERN and an elected member of the CERN Scientiﬁc Policy Committee from 1976 to 1982. In recent years, we often saw him at the SPC annual meetings to which former members are invited, and enjoyed the acute and humorous remarks he used to include in his interventions.

*John Iliopoulos and Luciano Maiani*

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^{(1)} His ﬁrst publication is entitled “Unitarity and causality in a renormalizable ﬁeld theory with unstable particles”, Physica, Vol. 29, 186 (1963).

^{(2)} He even joined Bernardini’s neutrino experiment for a while.