**Half a century ago, physicists found the route to a modern particle theory. At a conference in Amsterdam. Almost unnoticed, just before lunch and the tourist outing.**

The date is Saturday, July 3, 1971. Sometime in the morning. The place: a small room at the RAI in Amsterdam. That much those involved remember half a century on. But in the proceedings of the Amsterdam Conference on Elementary Particles, from 30 June to 6 July, the historic breakthrough is completely missing.

The reason, writes science historian and physicist Frank Close in his detailed book *The Infinity Puzzle* (2011), is that the contribution was only added to the program at the very last minute. “And now I introduce Mr. ‘t Hooft, who has a theory that is at least as elegant as anything we’ve heard before,” said chairman Tini Veltman. The rest is history, literally.

PhD student Gerard ‘t Hooft of Utrecht University gets to spend the last fifteen minutes of the morning session quickly presenting a new result. Then lunch and a bus trip to Volendam and Marken are on the program. It is slightly cloudy but warm and dry that afternoon.

‘t Hooft’s transparencies are blotchy due to sweaty hands and a bad marker, but his story that morning is rock solid as far as it can be followed. He shows that it is possible to construct a so-called Yang Mills field theory, in which infinities are avoided and force particles can have mass.

This is new. Physicists have been struggling for years with the question of how to construct a decent field theory with anything other than massless charged force carriers. The time-honored quantum theory of electromagnetism (QED) has photons, massless and uncharged light particles.

That theory has long had problems because direct computation quickly bogged down in infinities rather than realistic physics. Theorists Yang and Mills solved that problem in the 1950s. But only for particles without mass.

Renormalizable Lagrangians for massive Yang-Mills fields is the title of ‘t Hooft’s contribution published in Nuclear Physics a few weeks after the conference in Amsterdam. It is the basis for the Nobel Prize in physics that he and his supervisor Tini Veltman will receive in 1999. For mathematically describing the electroweak force, the force carried by massive W and Z particles.

To accomplish that, in 1971, ‘t Hooft combined Yang-Mills field theory with a then-new idea from theoretical physics: the mechanism now simply named after Peter Higgs. In it, an additional universal medium gives particles their mass.

That addition of the Higgs mechanism, ‘t Hooft and Veltman are the first to find out in 1971, does not interfere with Yang and Mills’ theory, and still allows for massive force particles like the W and the Z. The route to a useful theory of electroweak interaction is found. The W and Z are found at CERN in the 1980s.

‘t Hooft’s story in Amsterdam did not immediately make a huge impression, possibly due to the timid appearance of the young Dutch PhD student among many of the greats in the field. It seems unlikely that he would be the one to present the long-sought breakthrough in just a few sheets, and many people only realize this later, Close notes.

In the years following the breakthrough, others found a valid theory for the strong nuclear force, the third fundamental force in the particle world, in a similar manner. The so-called Standard Model is a fact, a useful theory that describes interactions in the subatomic world and stands up proudly in the vast majority of experiments.

In 2012, the Higgs particle was found at CERN, definitively proving the existence of the universal Higgs field, the essential ingredient of ‘t Hooft and Veltman’s theory.

‘t Hooft’s 1971 paper (in Nuclear Physics) is still one of the most cited papers in theoretical physics. He has not kept the overheads of his lecture in Amsterdam.

*(Master storyteller Frank Close gave an online lunch talk at Nikhef on June 30 about the tricky theoretical run-up to modern particle theory and the 1971 breakthrough. Recordings of that meeting can be viewed here).*