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Paul Adrien Maurice Dirac8.8.1902

Wikipedia (26 Jul 2013, 09:57)

Paul Adrien Maurice Dirac, OM, FRS (/dɪˈræk/ di-RAK; 8 August 1902 – 20 October 1984) was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. 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.

Among other discoveries, he formulated the Dirac equation, which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the Nobel Prize in Physics for 1933 with Erwin Schrödinger, "for the discovery of new productive forms of atomic theory." He also did work that forms the basis of modern attempts to reconcile general relativity with quantum mechanics.

He was regarded by his friends and colleagues as unusual in character. Albert Einstein said of him "This balancing on the dizzying path between genius and madness is awful" referring to his autistic traits. His mathematical brilliance, however, means he is regarded as one of the most significant physicists of the 20th century.


Honours

Dirac shared the 1933 Nobel Prize for physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory." Dirac was also awarded the Royal Medal in 1939 and both the Copley Medal and the Max Planck medal in 1952. He was elected a Fellow of the Royal Society in 1930, an Honorary Fellow of the American Physical Society in 1948, and an Honorary Fellow of the Institute of Physics, London in 1971. Dirac became a member of the Order of Merit in 1973, having previously turned down a knighthood as he did not want to be addressed by his first name.


Career

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 particle - i.e. 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 Clark Maxwell equations of electromagnetism.


Gravity

He quantized the gravitational field, and developed a general theory of quantum field theories 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 daily use the concepts and equations that he developed. 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, which leaned heavily on Bohr's correspondence principle but changed the equations so that they involved directly observable quantities. Fowler sent Heisenberg's paper on to Dirac, who was on vacation in Bristol, asking him to look into this paper carefully.


Quantum theory

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 recognized that this mathematical form had the same structure as the Poisson Brackets that occur in the classical dynamics of 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.

Dirac noticed an analogy between the Poisson brackets of classical mechanics and the recently proposed quantization rules in Werner Heisenberg's matrix formulation of quantum mechanics. This observation allowed Dirac to obtain the quantization rules in a novel and more illuminating manner. For this work, published in 1926, he received a Ph.D. from Cambridge.


The Dirac Equation

In 1928, building on 2×2 spin matrices which he discovered independently of Wolfgang Pauli's work on non-relativistic spin systems, (Abraham Pais quoted Dirac as saying "I believe I got these (matrices) independently of Pauli and possibly Pauli got these independently of me") he proposed the Dirac equation as a relativistic equation of motion for the wavefunction of the electron. 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. 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), however, led to a reinterpretation of Dirac's equation as a "classical" field equation for any point particle of spin ħ/2, itself subject to quantization 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 field equation 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 polarization in the early 1930s. This work was key to the development of quantum mechanics by the next generation of theorists, and in particular Schwinger, Feynman, Sin-Itiro Tomonaga and Dyson in their formulation of quantum electrodynamics.

Dirac's 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 Schrödinger on 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, he also included the bra-ket notation in the third edition of his book, thereby contributing to its universal use nowadays.


Magnetic monopoles

In 1933, following his 1931 paper on magnetic monopoles, Dirac showed that the existence of a single magnetic monopole in the universe would suffice to explain the observed quantization of electrical charge. In 1975, 1982, and 2009 intriguing results suggested the possible detection of magnetic monopoles, but there is, to date, no direct evidence for their existence.


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 enrichment by gas centrifuge.

Dirac's quantum electrodynamics made predictions that were – more often than not – infinite and therefore unacceptable. A workaround known as renormalization 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!" His refusal to accept renormalization 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, using the Heisenberg picture and without using the joining method used by Weisskopf and French, the two pioneers of modern QED, Schwinger and Feynman, in 1963. 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. 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 in order 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 based on lectures that he delivered at the 1949 International Mathematical Congress in Canada. Dirac had also solved the problem of putting the Tomonaga–Schwinger equation into the Schrödinger representation 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).

In the late 1950s, he applied the Hamiltonian methods he had developed to cast Einstein’s general relativity in Hamiltonian form and to bring to a technical completion the quantization 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 quantization of curved spacetime. He also published a paper entitled “Quantization of the Gravitational Field” in the 1967 ICTP/IAEA Trieste Symposium on Contemporary Physics.


   
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