Genius smiles quietly

The Collected Works of P.A.M. Dirac

September 27, 1996

Paul Adrien Maurice Dirac is regarded by physicists as one of the immortals of modern physics, ranking alongside the likes of Neils Bohr, Albert Einstein, Werner Heisenberg and Erwin Schrodinger, in recognition of his contribution to the development of quantum theory. It always seems surprising that he is not a household name like Einstein.

Dirac was arguably Britain's most outstanding theoretical physicist since Newton; and his most striking discovery - the existence of the dual world of antimatter - is known to millions round the world via the anti-matter drive of the Starship Enterprise. When Dirac retired from Cambridge he moved to Florida State University in the United States for the remainder of his life. One of his colleagues in Florida, Joseph Lannutti, describes his emotions on first hearing Dirac lecture: "Having studied and worked in physics for many years, the name Dirac was a basic constituent, an integral part of the warp and woof of my understanding of physics. Dirac was not a person. Dirac was an equation, a theory of antimatter, a delta function, a monopole or a kind of statistics."

R. H. Dalitz has done a great service to the scientific community in collecting together the published works of Dirac. The volume covers 1924-48 and a second one is planned to cover his later publications. Dalitz divides the papers in this period into three parts: "The early years", "The golden years" and "The war years".

"The golden years" begin with a reproduction of the front page of the proof copy of Heisenberg's first paper on the "New quantum theory". Dirac's supervisor Ralph Fowler sent this to him with a scribbled question: "What do you think of this? I shall be glad to hear. R. H. F." Dirac later said that it took him two weeks to realise that "non-commutation" was the most important idea introduced by Heisenberg. On one of his solitary Sunday walks he realised that this must be connected with classical Poisson brackets but that he"did not know very well what a Poisson bracket was, so was very uncertain of the connection". Unfortunately for Dirac all the libraries were closed and he had to wait impatiently for Monday morning. All of Dirac's seminal contributions to the foundations of quantum mechanics may be found in the next few papers - Poisson brackets and q numbers - "where q stands for quantum or maybe queer" - and his "darling" transformation theory. Max Born, who introduced the probability interpretation of the quantum wave-function, described his reaction on receiving Dirac's first paper: "This was one of the greatest surprises of my scientific life. For the name Dirac was completely unknown to me, the author appeared to be a youngster, yet everything was perfect in its way and admirable." There is also an algebraic solution of the hydrogen atom problem with not a wave function in sight. In a later paper, Dirac used his transformation theory to make clear the connection between Heisenberg's matrix mechanics and Schrodinger's wave-functions.

Just how remarkable a PhD student Dirac was can be seen from the contents and preface to his thesis. This is clearly a precursor to his famous book, The Principles of Quantum Mechanics, first published in 1930, which has remained a bestseller to this day. I remember my surprise on finding the first chapter to be largely devoted to a discussion of polarised light. Dalitz includes an interesting history of the book's evolution and of the Russian edition, which has a preface from the publisher warning the reader that "this work contains many views and statements completely at variance with dialectical materialism". The third edition included Dirac's famous "bra" and "ket" notation. In the lectures on quantum mechanics that he gave in Cambridge for so many years, it is said that Dirac permitted himself a quiet smile as he introduced this nomenclature.

There are many other delights in this collection. For example, we can marvel at how casually he introduces his famous delta function, remarking that it "can be regarded as the limit of a sequence of functions" but that it can be used as a function in practically all circumstances "without getting incorrect results."

The 1928 paper containing the Dirac equation is here, with its successful prediction of electron spin. But the following papers show why Heisenberg wrote to Wolfgang Pauli later that year: "The saddest chapter of modern physics is and remains the Dirac theory." The problem was that Dirac's equation predicted that there should be negative energy states for the electron. In 1930 Dirac came up with the idea of the "Dirac sea" - the idea that almost all of these negative energy levels were occupied and that the few "holes" in the sea would behave like a particle of positive charge and energy. The papers show clearly the confusion of the time with Dirac's initial identification of these particles with protons. It is not until 1931, in a paper obscurely titled "Quantised singularities in the electromagnetic field" that Dirac takes the plunge and postulates the existence of an "antielectron". Most of this paper is concerned with another of Dirac's brilliant speculations, namely the possibility of magnetic monopoles and a connection between magnetic and electric charges.

It is perhaps less well known that Dirac laid the foundations of quantum field theory that provides the basis for our understanding of wave-particle duality. Dirac was also first to show how to calculate the famous Einstein A and B radiation coefficients and first to understand the relation of the symmetry of quantum wave-functions to quantum statistics. All these fascinating developments may be followed through this superb collection of papers, gathered from far and wide, some translated from French, German and Russian. Dalitz has also tracked down many of Dirac's wartime reports on isotope separation and they are published here for the first time. Dirac made several contributions of lasting importance in this field.

One final topic deserves a mention: the paper on "The Lagrangian in quantum mechanics", published in a deeply obscure Russian journal, is significant in that it contains the sentence that led Richard Feynman to the "path integral"' formulation of quantum mechanics.

No article about Dirac would be complete without a retelling of one of the many "Dirac stories". Rudolf Peierls, with whom Dirac worked during the war years, recounts the following tale. A colleague in Cambridge, H. R. Hulme, was walking with Dirac when something rattled in his coat pocket. Hulme apologised for the noise, explaining that he had a bottle of pills that was no longer full. After some time Dirac replied: "I suppose it makes the maximum noise when it is half full." Peierls was curious to know whether this incident predated Dirac's hole theory: alas, it took place much later. This volume constitutes a superb memorial to one of the greatest physicists of the 20th century. The collection assembled by Dalitz should surely have a place in every serious scientific library and will be an invaluable source text for physicists and historians of science.

Tony Hey is professor of computation, University of Southampton.

The Collected Works of P.A.M. Dirac

Editor - R. H. Dalitz
ISBN - 0 521 36231 8
Publisher - Cambridge University Press
Price - £175.00
Pages - 1,310

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