## Martinus Veltman (1931 – 2021)

# Father of his own school of physics

In 1969, theoretical physicist and Nobel Prize winner Martinus Veltman introduced what Gerard ’t Hooft calls the ‘Veltmanian phrasing’ to Utrecht University: a clear approach to make complex theories concrete, and therefore usable. “Veltman wanted to know how nature worked. The practical approach he used is his legacy in the field.”

Martinus Justinus Godefridus (Tini) Veltman began his scientific career in 1948, when he enrolled at Utrecht University to study Mathematics and Physics. He graduated in 1956, fulfilled his national military service obligation, then returned to Utrecht University to start his PhD research. He spent much of this time at CERN, the European organisation for sub-atomic physics research in Switzerland. He earned his PhD at Utrecht University in 1963, and eventually returned to the university as a Professor in 1966.

**Unconventional lectures**

Utrecht University’s professors emeritus Gerard 't Hooft and Bernard de Wit were both Veltman’s students, and later PhD candidates. De Wit remembers well how his mentor entered the academic community at the Institute for Theoretical Physics in 1966. “Veltman had a unique way of dealing with students. At the time, older professors were placed on a pedestal, but Veltman climbed down to our level. He was very open and accessible to students, and enjoyed talking with them.”

But above all, Veltman was an excellent lecturer. “He stood out from the rest”, says De Wit. “Undergraduate education in the Netherlands was a bit tedious back then. A lot of lecturers could talk *about* things, but they couldn’t always *explain* them. Veltman’s lectures were unconventional: he had the ability to clarify something before he’d explained the mathematics behind it. He used his hands to explain things, so you really understood what the things meant.”

De Wit: “Then the faculty formed a committee to evaluate the entire undergrad curriculum. Veltman was appointed chairman of the committee. It gave him an opportunity to modernise the entire curriculum, often with new lecturers, and even with courses on new subjects.”

**Making Yang-Mills theory consistent with quantum mechanics**

Veltman’s main scientific wish was to formulate a field theory that could be used to describe ‘weak interactions’. De Wit: “They’re for example what causes beta radiation, where an atomic nucleus emits an electron. At that time, there was only one field theory available: the theory of electromagnetic phenomena, or quantum electrodynamics. That theory includes photons; particles of light.”

Gerard ’t Hooft: “Veltman wanted to know how nature worked. The practical approach he used is his legacy in the field.” According to De Wit, Veltman worked much more intuitively than most other physicists at the time. “He didn’t like the formal work methods, in part because the alternatives were threatening to become more and more complicated. It’s with that attitude that he began his study of the Yang-Mills theory.”

When I started, Veltman had already made considerable progress with his theoretical ideas for making the Yang-Mills theory easier to use, and Schoonschip was already working well.

Many physicists, Veltman included, expected that the field theory for weak interactions would be a Yang-Mills theory. Instead of a single type of photon particle, the theory posited several different types of photons. The various photons were also subject to the effects of forces. It was clear that the Yang-Mills theory was considerably more complicated than quantum electrodynamics.

De Wit: “Yang-Mills theory seemed incompatible with quantum theory, so it didn’t seem to be suitable for describing the quantum mechanical processes caused by weak interactions. Every calculation of those processes came up with an nonsense answer, like zero or infinity.”

**Accuracy needed**

’t Hooft: “The subject required some complicated calculations. If you try to do that by hand, you can’t avoid making mistakes. But Veltman started using a computer for those calculations back when he worked at CERN. Computers in the 1960s were a lot more sluggish than they are today. If you wanted to do time-consuming calculations, you had to program in machine language, so Veltman developed his own computer program for that called *‘Schoonschip*’ (Clean Ship).”

Bernard de Wit and Gerard ’t Hooft began their PhD research with Veltman in the autumn of 1969. ‘t Hooft: “When I started, Veltman had already made considerable progress with his theoretical ideas for making the Yang-Mills theory easier to use, and Schoonschip was already working well.” But the results led him to conclude that his ideas about Yang-Mills didn’t work as well.

‘t Hooft wanted to improve the theoretical knowledge to make it possible to calculate the relevant processes. “Once we understood how we needed to approach the work, it was fairly easy to solve the difficulties. Veltman had to commute between Utrecht and the ‘big computer’ in Amsterdam, which was much more primitive than a simple smartphone today. One day, he came back all excited: ‘It seems like we’ve found something!’, he shouted, but some of the details still needed to be corrected. Everything was finished within a year.”

Once, Veltman helped organise a conference in Amsterdam, and he had ‘t Hooft give a presentation. “There were a lot of big names from the field in attendance, who I only knew from their work. People understood that the accuracy with which we worked was necessary to do the calculations. The conference had a fantastic atmosphere.”

**Thinking in diagrams**

’t Hooft remembers his PhD supervisor as an ‘intensive mentor’. “Veltman thought that you could only lay a foundation during lectures. He could phrase everything very clearly in his own ‘Veltmanian’ manner. But you did have to crawl inside his thought process to understand what he meant. He taught us to think in terms of diagrams. Many of his colleagues worked with the most complicated formulas. Later on, I tried to pass on his way of formulating things to my own PhD candidates.” In 1973, Veltman and ‘t Hooft were to publish a book together titled ‘Diagrammar’, in which they explained the grammar of diagrams.

The theoretical school for particle physics in the Netherlands was set up by Veltman. Diagrammar is now a classic in the field, and is a standard textbook that I and many others have read during our studies.

Veltman was the person who challenged ‘t Hooft to make his work more tangible. “Veltman reminded me that an elementary particle is really a thing that goes from the machine where it’s created to the detector, through a space where it collides with other particles. When the detector says ‘click’, then you know the particle’s arrived. When I’d come to him with all sorts of calculations, he’d always want to know: when does it say ‘click’?”

**Nobel Prize**

Veltman realised better than most that the experiments like those conducted at CERN were vital to confirming his calculations. For decades, particle physicists in the Netherlands had been participating in the analysis of those experiments, but they did not play a significant role in developing the necessary equipment. De Wit: “Tini took the initiative to found the Nikhef Institute in the 1970s, as a collaborative effort between several Dutch universities. They still develop equipment for experiments at CERN. In so doing, the Netherlands makes an important contribution to the international research at CERN.”

In 1981, Veltman went to the US to lead a chair group at the University of Michigan. He worked there until he retired in 1996, when he returned to Bilthoven, near Utrecht. In 1999, Martinus Veltman and Gerard ’t Hooft were presented with the Nobel Prize in Physics for their work on the standard model of elementary particles in the early 1970s.

The high quality of physics research in Utrecht since the 1970s has since inspired a new generation of theoretical physicists to come to Utrecht University. Physicists such as Stefan Vandoren, who began working at the university as a junior researcher in 2000, and served as the Scientific Director of the ITF from 2012 to 2018. “The theoretical school for particle physics in the Netherlands was set up by Veltman. *Diagrammar* is now a classic in the field, and is a standard textbook that I and many others have read during our studies. The field has since made great strides, and we have some very strong research groups here in the Netherlands, but Veltman is the person who laid the foundation.“

Bernard de Wit visited Veltman’s home regularly since he retired to chat about their field. Smiling: “He used to think that he knew everything he needed to know, but over the past few years he occasionally took the trouble to ask us for our opinions.” Martinis Veltman passed away on Monday, 4 January 2021 at the age of 89.