It is a sublime moment when a great scientific discovery emerges at about the same time from the independent work of different scientists. This was the case with the discovery which led to the 1965 Physics Nobel Prize awarded to **Richard Feynman**, **Julian Schwinger**, and **Sin-itiro Tomanaga**. The trio won the prize for their path-breaking theoretical work in “taming” infinities in quantum mechanics, the preeminent theory that governs the behavior sub-atomic particles.

The 1965 award was the culmination of work that started in the 1930s when physicists were excitedly trying to unify the new theory of quantum mechanics with electromagnetism. The unified theory, known as **Quantum Electrodynamics** (QED), was supposed to offer a precise description of the interactions between matter and light. There was an annoying “bug” in the theory, however: every calculation using QED blew up into infinity, which contradicts reality.

The infinity problem was finally solved by the three Nobel laureates at nearly the same time. Schwinger’s highly mathematical solution was published as a one-page note in the February 1948 issue of the *Physical Review*. A sparkling genius in a field of geniuses, Schwinger became the youngest full professor at Harvard at the age of 29.

Working independently, Richard Feynman at Caltech developed his own solution using his cartoonish “Feynman diagrams” (an example is shown below).

Meanwhile, half-way across the world, the Japanese physicist, Sin-itiro Tomanaga solved the infinity problem, using techniques similar Schwinger’s but with a clearer and simpler formalism.

The QED story isn’t complete without mentioning the contribution of another theoretical physicist: **Freeman Dyson**. Dyson’s accomplishment was to unify the seemingly disparate solutions of the three Nobel laureates. An Englishman by birth, he was already famous in England in his twenties for his mathematical prowess. In the spring of 1948, Dyson came across, through Robert Oppenheimer, the first issue of the new journal, *Progress in Theoretical Physics*. Remarkably, that issue (1946) contained Tomanaga’s paper resolving the infinity issue, a paper which Dyson regarded as very lucidly written. Well aware of the work that Schwinger and Feynman had done, Dyson set about to find the interconnections of three papers. By October 1948, before Feynman’s masterpiece was published, Dyson finished his paper, “The radiation theories of Tomanaga, Schwinger, and Feynman”, proving their equivalence. This paper appeared in the *Physical Review* in February 1949.

Dyson followed his 1949 paper with another seminal work early that same year. In this second paper, he showed that once the infinities in QED were tamed, there were no other infinities that would result in higher-order calculations, completing what became known as the *renormalization* proof. Simply put, Dyson proved that once all quantities in QED theory were expressed in re-normalized physically measured masses and charges, all calculations and predictions of that theory were finite and sensible. It’s hard to overstate the importance of Dyson’s contributions; his result was not only reassuring, it provided the springboard through which Feynman’s diagrams would change the way future generations of physicists would view quantum physics. There is no doubt Dyson would have been a Nobel laureate, if not for the Nobel committee’s arbitrary rule that not more than three persons can share a Nobel Prize.

**The Seminal Papers**

Dyson, Freeman, J. (1949), “The Radiation Theories of Tomonaga, Schwinger, and Feynman, *Phys. Rev*. 75, 486 – Published 1 February 1949

Feynman, Richard.P. (1949), “Space-Time Approach to Quantum Electrodynamics”, *Phys. Rev*. 76, 769 – Published 15 September 1949.

Schwinger, Julian (1948), “On Quantum-Electrodynamics and the Magnetic Moment of the Electron”, *Phys. Rev*. 73, 416 – Published 15 February 1948.

Tomonaga, S. (1946), “On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields”, *Progress in Theoretical Physics*, 1, 27-42- Published 1 August 1946.