Paul Adrien Maurice Dirac OM FRS[7] (/dɪˈræk/; 8 August 1902 – 20 October 1984) was an English theoretical physicist who is regarded as one of the most significant physicists of the 20th century.
Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory".[8] He also made significant contributions to the reconciliation of general relativity with quantum mechanics.
Dirac was regarded by his friends and colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote of Dirac, "This balancing on the dizzying path between genius and madness is awful".[9]
He was the Lucasian Professor of Mathematics at the University of Cambridge, a member of the Center for Theoretical Studies, University of Miami, and spent the last decade of his life at Florida State University.
Dirac established the most general theory of quantum mechanics and discovered the relativistic equation for the electron, which now bears his name. The remarkable notion of an antiparticle to each fermion particle – e.g. the positron as antiparticle to the electron – stems from his equation. He was the first to develop quantum field theory, which underlies all theoretical work on sub-atomic or "elementary" particles today, work that is fundamental to our understanding of the forces of nature. He proposed and investigated the concept of a magnetic monopole, an object not yet known empirically, as a means of bringing even greater symmetry to James Clerk Maxwell's equations of electromagnetism.
Gravity
He quantised the gravitational field, and developed a general theory of quantum fieldtheories with dynamical constraints, which forms the basis of the gauge theories and superstring theories of today. The influence and importance of his work has increased with the decades, and physicists use the concepts and equations that he developed daily.
Quantum theory
Dirac's first step into a new quantum theory was taken late in September 1925. Ralph Fowler, his research supervisor, had received a proof copy of an exploratory paper by Werner Heisenberg in the framework of the old quantum theory of Bohr and Sommerfeld. Heisenberg leaned heavily on Bohr's correspondence principle but changed the equations so that they involved directly observable quantities, leading to the matrix formulation of quantum mechanics. Fowler sent Heisenberg's paper on to Dirac, who was on vacation in Bristol, asking him to look into this paper carefully.
Dirac's attention was drawn to a mysterious mathematical relationship, at first sight unintelligible, that Heisenberg had reached. Several weeks later, back in Cambridge, Dirac suddenly recognised that this mathematical form had the same structure as the Poisson brackets that occur in the classical dynamicsof particle motion. From this thought he quickly developed a quantum theory that was based on non-commuting dynamical variables. This led him to a more profound and significant general formulation of quantum mechanics than was achieved by any other worker in this field.[54] Dirac's formulation allowed him to obtain the quantisation rules in a novel and more illuminating manner. For this work,[55]published in 1926, Dirac received a PhD from Cambridge. This formed the basis for Fermi-Dirac statistics that applies to systems consisting of many identical spin 1/2 particles (i.e. that obey the Pauli exclusion principle), e.g. electrons in solids and liquids, and importantly to the field of conduction in semi-conductors.
Dirac was famously not bothered by issues of interpretation in quantum theory. In fact, in a paper published in a book in his honour, he wrote: "The interpretation of quantum mechanics has been dealt with by many authors, and I do not want to discuss it here. I want to deal with more fundamental things."[56]
The Dirac equation
In 1928, building on 2×2 spin matrices which he purported to have discovered independently of Wolfgang Pauli's work on non-relativistic spin systems (Dirac told Abraham Pais, "I believe I got these [matrices] independently of Pauli and possibly Pauli got these independently of me."),[57] he proposed the Dirac equation as a relativistic equation of motion for the wave function of the electron.[58] This work led Dirac to predict the existence of the positron, the electron's antiparticle, which he interpreted in terms of what came to be called the Dirac sea.[59] The positron was observed by Carl Anderson in 1932. Dirac's equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon.
The necessity of fermions (matter) being created and destroyed in Enrico Fermi's 1934 theory of beta decay led to a reinterpretation of Dirac's equation as a "classical" field equation for any point particle of spin ħ/2, itself subject to quantisation conditions involving anti-commutators. Thus reinterpreted, in 1934 by Werner Heisenberg, as a (quantum) field equation accurately describing all elementary matter particles – today quarks and leptons – this Dirac fieldequation is as central to theoretical physics as the Maxwell, Yang–Mills and Einstein field equations. Dirac is regarded as the founder of quantum electrodynamics, being the first to use that term. He also introduced the idea of vacuum polarisation in the early 1930s. This work was key to the development of quantum mechanics by the next generation of theorists, in particular Schwinger, Feynman, Sin-Itiro Tomonaga and Dyson in their formulation of quantum electrodynamics.
Dirac's The Principles of Quantum Mechanics, published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics and of Erwin Schrödingeron wave mechanics into a single mathematical formalism that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system. The book also introduced the delta function. Following his 1939 article,[60] he also included the bra–ket notation in the third edition of his book,[61]thereby contributing to its universal use nowadays.
Magnetic monopoles
In 1931, Dirac proposed that the existence of a single magnetic monopole in the universe would suffice to explain the quantisation of electrical charge.[62] In 1975,[63] 1982,[64] and 2009[65][66][67] intriguing results suggested the possible detection of magnetic monopoles, but there is, to date, no direct evidence for their existence (see also Magnetic monopole#Searches for magnetic monopoles).
Lucasian Chair
Dirac was the Lucasian Professor of Mathematics at Cambridge from 1932 to 1969. In 1937, he proposed a speculative cosmological model based on the so-called large numbers hypothesis. During World War II, he conducted important theoretical and experimental research on uranium enrichmentby gas centrifuge.
Dirac's quantum electrodynamics (QED) made predictions that were – more often than not – infinite and therefore unacceptable. A workaround known as renormalisation was developed, but Dirac never accepted this. "I must say that I am very dissatisfied with the situation", he said in 1975, "because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small – not neglecting it just because it is infinitely great and you do not want it!"[68] His refusal to accept renormalisation resulted in his work on the subject moving increasingly out of the mainstream.
However, from his once rejected notes he managed to work on putting quantum electrodynamics on "logical foundations" based on Hamiltonian formalism that he formulated. He found a rather novel way of deriving the anomalous magnetic moment"Schwinger term" and also the Lamb shift, afresh in 1963, using the Heisenberg picture and without using the joining method used by Weisskopf and French, and by the two pioneers of modern QED, Schwinger and Feynman. That was two years before the Tomonaga–Schwinger–Feynman QED was given formal recognition by an award of the Nobel Prize for physics.
Weisskopf and French (FW) were the first to obtain the correct result for the Lamb shift and the anomalous magnetic moment of the electron. At first FW results did not agree with the incorrect but independent results of Feynman and Schwinger.[69] The 1963–1964 lectures Dirac gave on quantum field theory at Yeshiva University were published in 1966 as the Belfer Graduate School of Science, Monograph Series Number, 3. After having relocated to Florida to be near his elder daughter, Mary, Dirac spent his last fourteen years (of both life and physics research) at the University of Miami in Coral Gables, Florida, and Florida State University in Tallahassee, Florida.
In the 1950s in his search for a better QED, Paul Dirac developed the Hamiltonian theory of constraints[70] based on lectures that he delivered at the 1949 International Mathematical Congress in Canada. Dirac[71]had also solved the problem of putting the Tomonaga–Schwinger equation into the Schrödinger representation[72] and given explicit expressions for the scalar meson field (spin zero pion or pseudoscalar meson), the vector meson field (spin one rho meson), and the electromagnetic field (spin one massless boson, photon).
The Hamiltonian of constrained systems is one of Dirac's many masterpieces. It is a powerful generalisation of Hamiltonian theory that remains valid for curved spacetime. The equations for the Hamiltonian involve only six degrees of freedom described by 
,
for each point of the surface on which the state is considered. The 
(m = 0, 1, 2, 3) appear in the theory only through the variables 
, 
which occur as arbitrary coefficients in the equations of motion. There are four constraints or weak equations for each point of the surface 
= constant. Three of them 
form the four vector density in the surface. The fourth 
is a 3-dimensional scalar density in the surface HL ≈ 0; Hr ≈ 0 (r = 1, 2, 3)
, for each point of the surface on which the state is considered. The (m = 0, 1, 2, 3) appear in the theory only through the variables , which occur as arbitrary coefficients in the equations of motion. There are four constraints or weak equations for each point of the surface = constant. Three of them form the four vector density in the surface. The fourth is a 3-dimensional scalar density in the surface HL ≈ 0; Hr ≈ 0 (r = 1, 2, 3)
In the late 1950s, he applied the Hamiltonian methods he had developed to cast Einstein's general relativity in Hamiltonian form[73] and to bring to a technical completion the quantisation problem of gravitation and bring it also closer to the rest of physics according to Salam and DeWitt. In 1959 he also gave an invited talk on "Energy of the Gravitational Field" at the New York Meeting of the American Physical Society later published in 1959 Phys Rev Lett 2, 368. In 1964 he published his Lectures on Quantum Mechanics(London:Academic) which deals with constrained dynamics of nonlinear dynamical systems including quantisation of curved spacetime. He also published a paper entitled "Quantization of the Gravitational Field" in the 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics.
Professorship at Florida State University
From September 1970 to January 1971, Dirac was Visiting Professor at Florida State University in Tallahassee. During that time he was offered a permanent position there, which he accepted, becoming a full professor in 1972. Contemporary accounts of his time there describe it as happy except that he apparently found the summer heat oppressive and liked to escape from it to Cambridge.[74]
He would walk about a mile to work each day and was fond of swimming in one of the two nearby lakes (Silver Lake and Lost Lake), and was also more sociable than he had been at Cambridge, where he mostly worked at home apart from giving classes and seminars; at FSU he would usually eat lunch with his colleagues before taking a nap.
Dirac published over 60 papers in those last twelve years of his life, including a short book on general relativity. His last paper (1984), entitled "The inadequacies of quantum field theory," contains his final judgment on quantum field theory;
"These rules of renormalisation give surprisingly, excessively good agreement with experiments. Most physicists say that these working rules are, therefore, correct. I feel that is not an adequate reason. Just because the results happen to be in agreement with observation does not prove that one's theory is correct."
The paper ends with these words;
"I have spent many years searching for a Hamiltonian to bring into the theory and have not yet found it. I shall continue to work on it as long as I can and other people, I hope, will follow along such lines."
(Source: "Paul Dirac: The Man and his Work" by Abraham Pais et al.)
Students
Amongst his many students[75][3] were Homi J. Bhabha[2], Fred Hoyle and John Polkinghorne.[4] Polkinghorne recalls that Dirac "was once asked what was his fundamental belief. He strode to a blackboard and wrote that the laws of nature should be expressed in beautiful equations."[76]
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