Robert Mills

Robert Laurence Mills was born in Englewood, New Jersey, in 1927. He took his bachelor's at Columbia in 1948 and his PhD at Columbia in 1955 under Norman Kroll, with a dissertation on quantum electrodynamics of bound states. The decisive event of his career came in the summer of 1953, before he had even finished the thesis: as a postdoctoral fellow at Brookhaven National Laboratory, Mills shared an office with the visiting Chen-Ning Yang from the Institute for Advanced Study, and the two of them, in the course of conversations about how to extend gauge theory beyond the abelian U(1) of electromagnetism, worked out the construction now called Yang-Mills theory.

The collaboration was a genuine fifty-fifty partnership. Mills's own two-page recollection (published in *American Journal of Physics* in 1989) describes the work plainly: Yang had been thinking for some years about whether isospin symmetry — the SU(2) symmetry that interchanged protons and neutrons — could be made into a *local* gauge symmetry the way the U(1) of QED was. The mathematics had stalled because the resulting field strength tensor was not simply F_{μν} = ∂_μ A_ν − ∂_ν A_μ but acquired a non-linear self-interaction term g f^{abc} A^b_μ A^c_ν reflecting the non-commutativity of the SU(2) generators. Yang and Mills worked through the construction over several weeks at Brookhaven, derived the modified field equations and the modified Bianchi identity, recognised that the resulting gauge bosons had to be massless (which was an obvious problem if the symmetry was supposed to describe the short-range strong force), and submitted the paper to *Physical Review* in October 1953. It was published in 1954.

After Brookhaven, Mills joined the Ohio State University faculty in 1956 and remained there for the rest of his career, becoming full professor in 1962 and retiring in 1995. His subsequent work was in the same area — gauge field theory, statistical mechanics, theoretical condensed matter — but never approached the impact of the 1954 paper, which became progressively more important as the Standard Model took shape in the late 1960s and 1970s. Mills was modest about the partnership and consistently deferred to Yang, both because Yang had been the senior figure on the original problem and because Yang's later work (parity violation, the Yang-Baxter equation, sustained leadership of theoretical physics for half a century) gave him a more visible scientific career. Mills died of cancer in 1999 in Charlestown, West Virginia. The Yang-Mills construction is the mathematical backbone of every gauge theory in modern physics: SU(2) for the weak force, SU(3) for the strong force, SU(3)×SU(2)×U(1) for the Standard Model as a whole.