cphil_gluons

Julian Schwinger had the ideal background to pick up the Yang-Mills concept and apply it to the weak and electromagnetic interactions. He was something of a child prodigy in mathematics. He was born in 1918 and entered the City College of New York at the age of fourteen, then transferred to Columbia University, where he gained his B.A. at the age of seventeen, and a Ph.D. degree three years later. He worked with Robert Oppenheimer (the “father of the atomic bomb”) at the University of California, then at the University of Chicago and at MIT before joining the faculty of Harvard University in 1945. A year later, at the age of twenty-eight, he became one of the youngest full professors ever appointed to the august university. Schwinger made major contributions to the development of QED, and in 1965 he shared the Nobel Prize in Physics with Richard Feynman and Sin-Itiro Tomonaga, of Tokyo University, for his work. But the rules of the game are slightly different with weak interaction. In beta decay, for example, a neutron is converted into a proton, so the isotopic spin (isospin) symmetry is disturbed. But at the same time, in such an interaction, a neutrino is converted into an electron (or anti-neutrino and an electron are created together, which is the same thing.), so there has been a transformation in the lepton world analogous to the isospin change in the hadron world. This leads to the idea of “weak isospin”, a quantum parameter like isospin but one that applies to leptons as well as to hadrons. In 1957, Schwinger took over the non-Abelian local gauge theory developed by Yang and Mills for strong interaction and applied it to the weak interaction and electromagnetism (QED) together. Like the Yang and Mills, Schwinger’s version had three vector bosons, one without charge and the other two carrying charge. And like Yang and Mills, Schwinger identified the uncharged field quanta with photons. But, unlike Yang and Mills, in Schwinger’s treatment the two charged vector bosons were regarded as the W⁺ and W^–, the carriers of the weak force. There was still the problem with masses. Masses had to be added to the theory for the W particles more or less by hand, on an ad hoc basis. But this theory, in spite of its obvious flaws, again raised interesting new ideas. It implied that the weak force and the electromagnetic force were “really” the same strength as each other, in some sense symmetric, but the symmetry had gotten lost, or was broken, because the W particles had mass (and therefore a limited range) while the photon had none (and therefore of infinite range).

This led to two lines of development in field theory. Sidney Bludman of the University of California at Berkeley took up the links with Yang-Mills theory and pointed out in 1958 that the weak force alone could be described by a local, non-Abelian gauge theory with three particles, the W⁺, the W^–, and a third vector boson, with zero charge, which he called Z⁰ or simply Z. This left electromagnetism completely out of the picture for the time being, but carried with it the implication that there ought to be a weak interactions that involved no change in electric charge — ones that are mediated by the Z particle and are known as neutral current interactions. All these quanta are massless in the Bludman’s model, so the model was far from being realistic. It was far from the “answer” than the earlier models.

Meanwhile, Sheldon Lee Glashow, a physicist who had been born in the Bronx in 1932 and graduated from Cornell University in 1954, had been studying for his Ph.D. degree at Harvard under the supervision of Schwinger. Glashow found a way to take a Bludman’s version on the theme and combine it with a description of electromagnetism, producing a model, which he published in 1961. It included both a triplet of vector bosons to carry the weak force and a single vector boson to carry the electromagnetic force. The only immediate benefit of this approach was that it proved possible to ensure that the way the singlet and triplet mixed together produced one very massive neutral particle, the Z, and took all the mass away from the other one, the photon, instead of having two neutral particles that each had mass. But the mass still had to be put in by hand, to destroy the symmetry between the electromagnetic and weak forces in the basic question, and worst of all, the theory did not seem to be renormalizable but was plagued by the kind of infinities that cropped up in QED but are removed by suitable mathematical sleight of hand. The mathematical sleight of hand needed to put mass into the earlier electroweak models made it impossible to carry out the renormalization trick as well.

At the same time, starting out in the late 1950s and continuing into the early 1960s, the Pakistani physicist Abdus Salam and his colleague John Ward were developing an electroweak theory very similar to the one proposed by Glashow. Salam was born in Jhang, in what is now Pakistan, in 1926. After attending Punjab University he went on to Cambridge where he was awarded his Ph.D. degree in 1952, and taught in Lahore and at Punjab University until 1954, when he returned to Cambridge University and, among other things, supervised the work of student Ronald Shaw until 1954. Since the subject chosen by students for investigation usually reflects the interest of their supervisiors, Ronald Shaw’s work was no exception. Salam was interested in gauge theories of the basic forces of nature, along the lines of the Yang-Mills theory. In 1957 he took up the post as professor of theoretical physics at Imperial College in London, and in 1964 he was the moving force behind the establishment of the International Centre for Theoretical Physics in Trieste, an institute that provides research opportunities for physicists from developing countries. Since then, Salam has been director of the Centre in Trieste and spent some his time there and some at the Imperial College.

Salam and his colleague Ward developed a variation on the electroweak theme (Later John Ward, a British physicist, worked at several U.S. institutionsin the 1960s, including John Hopkins University); it suffered from the same defects as Glashow’s version — the masses had to be put in by hand, and largely as a result of this, it was impossible to renormalize the theory. The first step toward solving this problem was taken in 1967, when Salam and, independently, the American physicist, Steven Weinberg, found a way to make the masses of the weak vector bosons to appear naturally (well, almost naturally) out of the equations. The trick involved spontaneous symmetry breaking, and once again it depended upon ideas that had been developed initially in the context of the strong field.

Symmetry breaking can be easily understood by looking at the weak gravity field of the earth. To an astronaut in free fall in a spacelab, there is no special direction in space. If the astronaut lets go of a pen, it floats off in the particlar direction in space that the astronaut pushes it. All directions are equivalent; there is a basic symmetry. However, on the surface of the earth, things are different. If you give the pen a push in any direction and let go of it, it always falls the same way, downwards. “Downwards” means toward the center of the earth. Drop a pen at the North Pole, it falls downwards; drop a pen at the South Pole, it falls downwards. But the two “downwards” are opposite in direction to one another. The basic symmetry is hidden, or broken by the earth’s gravitational field.

Another form of hidden symmetry can be seen by another example, involving gravity again. Imagine a perfectly smooth, symmetrical surface shaped like a Mexican hat, with the brim turned up. If the “hat” rests upon a horizontal surface, it is completely symmetrical in the earth’s gravitational field. Now imagine placing a small, round ball on the top of the hump in the middle of the hat. Everything is perfectly symmetrical as long as the ball does not move. But we know what will actually happen in such a situation. The ball is unstable, balanced at the highest point of the hump, and it will soon roll off and roll down the side of the hump to rest in the rim of the hat. Once this happens, the hat and ball are no longer symmetrical. The unstable symmetry is broken. There is a special direction associated with the system, a direction defined by a line pointing outward from the center of the hat through the place where the ball rests on the rim. The system is now stable, in the lowest energy state that it can reach, but it is no longer symmetrical. It turns out that the masses associated with the field quanta in a Yang-Mills type of theory can arise from a similar symmetry breaking involving the abstract “internal space” in which the arrows of isospin point.

The idea gradually brewed up in the 1950s and 1960s from the work of several theoretical physicists, but it came to full flower with the work of Peter Higgs at the University of Edinburgh between 1964 and 1966. Higgs, who was born in 1929, had studied at King’s College in London from 1947 onward and received his Ph.D. in 1954. He took up a post in Edinburgh in 1960. Higgs proposed that there must be an extra field added to the Yang-Mills model, one that had the unusual property that it does not have the least possible energy when the value of the field is zero, but when the field has a value bigger than zero. The electromagnetic field, and most other fields, have zero energy when the value of the field is zero, and the state in which all fields have minimum energy is what we call the vacuum. If all fields were like the electromagnetic field,that would be the same as saying that in the vacuum state all fields are zero. But the Higgs field has a nonzero value even in its state of minimum energy, and this gives the vacuum itself a character it would not otherwise possess. Reducing the Higgs field to zero would actually involve putting energy into system.

The implications of this is profond. In terms of isospin, the Higgs field provides a frame of reference, a direction against which the arrow defines proton and neutron can be measured. A proton can be distinguished from a neutronby comparing the direction of its isospin arrow with the direction defined by the Higgs field. But when the isospin arrow rotates during a gauge transformation, the Higgs arrow rotates as well, so that the angle stays the same. The angle that used to correspond to a proton now corresponds to a neutron, and vice versa. Without the Higgs mechanism, there would be no way to tell the difference between proton and neutron at all, because there would be nothing to measure their different isospin against. All that can be measured is the relative arrow between the isospin and the Higgs arrow, not any absolute orientation of isospin. And the Higgs field does this even though the field itself is a scalar, which has only magnitude, and does not point in any preferred direction at each point of “real” space.

The effect of all this on the vector boson is dramatic. There are four scalar Higgs boson required by the field theory, and the basic Yang-Mills approach gives three massless vector bosons. When the two elements are put together, three of the Higgs boson and three vector bosons merge with one another — in the graphic terminology used by Abdus Salam — the vector bosons “eat” one Higgs bosons. And when this happens, the vector bosons gains both mass and a spin corresponding to the spin carried by Higgs bosons. Instead of having three massless vector bosons and three four Higgs particles, the theory predicts that there should be three observable vector bosons that each have a definite mass, plus one scalar Higgs boson, which also has a large mass but whose precise mass cannot by the theory. The Higgs field breaks the underlying symmetry in just the right way to fit in with what we observe. At the cost of one extra undetected particle, mass appears naturally in all the variations in the Yang-Mills approach.

Higgs himself had been working in the context of the strong field. But soon his ideas were taken over into the developing electroweak theory. First off the mark was Steven Weinberg in 1967. Weinberg had been an exact contemporary of Glashow (although he was six months the younger, having been born in May 1933) at the Bronx High School of Science, from which Weinberg graduated in 1950, and Cornell University, where he graduated in 1954. But then he followed a different path to end up with a model very similar to Glashow’s description of the electroweak interaction, but with the bonus of a Higgs-type mechanism included. By 1960 Weinberg arrived at Berkeley, where he stayed until 1969 before moving on first to MIT and then, in 1973, to Harvard. Weinberg’s approach to electroweak unification was largely his own, but drawing upon the same culture — the same background pool of knowledge — that Glashow and Salam were drawing on. His interest in the weak interaction went back to his Ph.D. work at Princeton, and in the 1960s he worked toward an equivalent of the Higgs mechanism in his own way. His electroweak model, including masses for the vector bosons generated by spontaneous symmetry breaking, was submitted for publication in October 1967 and appeared in the journal Physical Review Letters before the end of year.

Salam heard about the Higgs mechanism from a colleague at Imperal College a few months before Weinberg submitted that paper for publication. Salam took the electroweak model that he developed with Ward and added the Higgs mechanism to it, giving essentially the same basic model that Weinberg had developed, with the masses now occurring naturally. He gave a series of lectures on the new model at the Imperial College in 1967, followed by a talk at the Nobel Symposium in May 1968, later published in the symposium proceedings.

In due course, in 1979. Glashow, Salam, and Weinberg joinly received the Nobel Prize in Physics for their role in creating the electroweak theory, a step as important as Maxwell’s development of the unified electromagnetic theory a century before. It took some time for even most theorists to appreciate fully the significance of the Weinberg-Salam model, because it was not until 1971 that a Dutch physicist, Gerald t’Hooft, showed that the electroweak theory was, indeed, renormalizable. And then, in 1973, experiments at CERN come up with evidence of the elusive neutral current interactions that the theory predicted, interaction mediated by the neutral Z particle. It was the normalization of gauge theory by t’Hooft that led to the explosive development of field theory in the 1970s, to a theory of the strong interactions, and to understanding what happened in earliest moments of the Universe itself.

In 1967-68, Steven Weinberg, Abdus Salam, and Sheldon Lee Glaslow noticed the amazing similarity between the photon and the W-particle. They made the following observation: Although Einstein had tried to unite light and the gravitational force, perhaps the correct unification scheme was to unite the photon and the W-particle. The result was a new W-particle theory, called the electro-weak theory, which differed decisively from the previous W-particle theories, because it used the most sophisticated form of gauge theory available at the time, the Yang-Mills theory. This theory, formulated in 1954, possessed more symmetries than Maxwell ever dreamed of. The Yang-Mills theory contained a new mathematical symmetry [represented mathematically as SU(2) × U(1)] that allowed Weinberg and Salam to unite the weak and electromagnetic forces on the same footing. This theory also treats the electron and the neutrino symmetrically as members of one “family”. As far as the theory was concerned, the electron and the neutrino were actually two sides of the coin. (But the theory did not explain why there was three redundant families.)

Although the Yang-Mills theory was the most ambitious and advanced theory of the time, it was ignored, because it was assumed that it was probably nonrenormalizable, like all other dead ends and therefore riddle with infinities. However, all that changed in 1971. After three decades of agonizing over the infinities festering within the W-particle theory, a dramatic break-through was made by a twenty-four-year-old Dutch graduate student, Gerard ‘t Hooft, who finally proved that the Yang-Mills theory was renormalizable. To double check his calculation showing the cancelation of infinities, ‘t Hooft placed the calculations on a computer. One can imagine the excitement that ‘t Hooft must have felt as he awaited the results of the calculations. He later recalled, “The results of that test were available by July 1971; the output of the program was an uninterrupted string of zeros. Every infinity canceled exactly.”

As the word of the cancelation spread, within months, hundreds of physicists rushed to learn the techniques of ‘t Hooft and the theory of Weinberg and Salam. For the first time, real numbers, not infinities, poured out of theory for S-matrix. Earlier, from 1968 to 1970, not a single paper published made reference to the theory of Weinberg and Salam. But by 1973, when the full impact of their results was being appreciated, 162 papers on the theory was published.

Somehow, in ways that physicists still do not completely understand, the symmetries built into the Yang-Mills theory completely eliminated the infinities that had plagued the earlier W-particle theory. It was a replay of the discovery made by the physicists studying QED years earlier; the symmetries somehow canceled the divergences in a quantum field theory.