Paul Dirac

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Paul Dirac 1933

Paul Adrien Maurice Dirac (born  August 8, 1902 in Bristol , †  October 20, 1984 in Tallahassee ) was a British physicist .

Dirac was a co-founder of quantum physics . In 1933 he was awarded the Nobel Prize in Physics . One of his most important discoveries is described in the Dirac equation of 1928, in which Einstein's special theory of relativity and quantum physics could be brought together for the first time. He also laid the foundations for the later detection of antimatter .


Dirac was born in Bristol , Gloucestershire , England . His father Charles Dirac was Swiss with roots in the French-speaking Saint-Maurice in Valais ; he taught French at Dirac's school in Bristol. His mother, Florence Holten, was the daughter of a Cornish seaman . His childhood was unhappy as a result of the strict and authoritarian behavior of his father - a brother took his own life.

Dirac first studied electrical engineering in Bristol in 1921 , then switched to mathematics and in 1923 received a scholarship to Cambridge University , where he studied with Ralph Howard Fowler . In 1926 he completed his studies with a dissertation on quantum mechanics .

Paul Dirac with his wife Margit
in Copenhagen in July 1963

From 1932 to 1969 Dirac was Professor of the Lucasische Chair of Mathematics at the University of Cambridge . In 1934 he worked as a visiting professor at the newly established Institute for Advanced Study (in Princeton, New Jersey, but separately from the university). In 1937 he married Margit (1904–2002), the sister of the physicist Eugene Wigner . The mathematician Gabriel Andrew Dirac from his wife's first marriage was his stepson. During the Second World War Dirac worked on gas centrifuges for uranium enrichment. From 1970 he worked at Florida State University in Tallahassee , Florida.

Dirac was reserved in nature. He didn't mind being silent in company and only giving very sparse answers to questions, committed to a strict love of truth, about which numerous anecdotes were common.

Dirac was a staunch atheist . When asked for his opinion on Dirac's views, Wolfgang Pauli remarked, alluding to the Islamic creed:

"If I understand Dirac correctly, he means the following: There is no God and Dirac is his prophet."


In 1925, Paul Dirac found the classical equivalent of the new quantum mechanical commutators from Heisenberg , Born and Jordan with the Poisson brackets of classical mechanics in his dissertation . In 1926 he developed an abstract version of quantum mechanics ("transformation theory"), which contained Heisenberg's matrix mechanics and Schrödinger's wave mechanics as special cases. Thus he was able to show the equivalence of both theories independently of Schrödinger. Classical mechanics results in his theory as a special case of quantum mechanics. Dirac also introduced the interaction image, which uses both the Schrödinger and Heisenberg images.

Paul Dirac on the blackboard

In 1928, based on the work of Wolfgang Pauli on the principle of exclusion, he set up the Dirac equation named after him, which is a relativistic first-order wave equation for the description of the electron based on the special theory of relativity . Dirac found it by starting from the relativistic wave equation of the 2nd order by Charles Galton Darwin (a further development of the Klein-Gordon equation ) and playing around a little with equations, that is, he was looking for an approach for a corresponding equation 1. Order that could only be obtained with the introduction of spinors and Dirac matrices and whose “square” again results in the relativistic wave equation. She delivered z. B. a theoretical explanation for the anomalous Zeeman effect and the fine structure in atomic spectroscopy and explained the spin , which until then was known in quantum mechanics as a fundamental but not understood phenomenon, as a natural consequence of its relativistic wave equation.

His equation also allowed Dirac to formulate the hole theory and to predict the existence of the positron , the antiparticle of the electron (but at first he shied away from the public postulation of a new particle and identified the negative antiparticle of the electron with the proton). The positron was then detected in 1932 by Carl David Anderson as a new particle in cosmic rays . In the Dirac picture of quantum field theory, the vacuum consists, in analogy to solid state physics, of a Dirac lake filled to the Fermi limit of electrons. Pair creation in a vacuum is the excitation of an electron from this Dirac Sea beyond the Fermi limit - the “hole” left behind in the Dirac Sea is the positron.

His 1930 published book The Principles of Quantum Mechanics (German Principles of Quantum Mechanics , 1930) pioneered the use of linear operators as a generalization ( "transformation theory") of the theories of Heisenberg and Schrödinger. With it, the delta functional (a special distribution , also called Dirac function or delta function) as well as the Bra-Ket notation was used, in which a state vector in the Hilbert space of a system is designated (e.g. initial state) and the vector that is dual to it (e.g. B. Final state in the description of a physical process). The above textbook has remained a standard work to this day and, in Dirac's eyes, was so perfect that he simply read from it in his lectures.

Dirac created the term boson in recognition of Satyendra Nath Bose's contribution to quantum statistics . Together with Enrico Fermi, he is considered to be the inventor of the statistics of fermions ( Fermi-Dirac statistics ), but recognized Fermi's priority.

In 1931 he was the first to postulate the existence of a magnetic monopole , i.e. a particle with a magnetic charge, similar to the electric charge z. B. the electron. The existence of such a particle, which has not yet been observed, would explain the quantization of the electric charge. Ultimately, this is based on topological ideas that appear here for the first time in quantum mechanics.

In his “ Large number hypothesis ” Dirac tries - more plausibly than similar attempts by Eddington - to give a connection between the size of the fundamental constants and the current expansion of the universe. This gives rise to speculations about the temporal variation of the natural constants, which have been investigated experimentally to this day. Dirac's big competitor in the field of quantum mechanical formalisms, Pascual Jordan , took up these ideas in his own theory of gravitation with a variable gravitational constant.

In his investigation of the classical theory of radiating electrons from 1938, not only “runaway solutions” but also renormalization ideas appeared for the first time. The appearance of divergent expressions in the usual renormalization theory of quantum electrodynamics, which are then made to disappear in the definition of “bare” charge and mass, he rejected all his life.

Paul Dirac, Wolfgang Pauli and Rudolf Peierls , 1953 in Birmingham

Dirac is also the inventor of many other formalisms in theoretical physics. For example, he originally came up with the idea of path integrals , which, as an alternative approach to quantum mechanics, were only “taken seriously” and expanded by Richard Feynman . In a work from 1949 he invented the "light cone quantization" (light front formalism) of quantum field theory, which is widely used in high-energy physics. In the 1950s, Dirac then tried to interpret the Dirac lake postulated by him as a universal ether .

He also examined generally Hamiltonian systems with “constraints”, especially in order to find an approach to the quantization of gravity. This work was later incorporated into the BRST formulation. His investigation of extended systems in quantum field theory in 1962 is a forerunner of the p-branes and bag models of later years.


Gravesite of Paul Dirac and his wife Margit in Roselawn Cemetery , Tallahassee , Florida
Green slate commemorative plaque in Westminster Abbey

In 1933 Dirac and Erwin Schrödinger received the Nobel Prize in Physics “for the discovery of a new, useful form of atomic theory ”. In 1930 he was elected as a member (" Fellow ") in the Royal Society , which awarded him the Royal Medal in 1939 and the Copley Medal in 1952 . He was elected to the USSR Academy of Sciences in 1931, the American Philosophical Society in 1938 , the Royal Society of Edinburgh in 1946 , the National Academy of Sciences in 1949, and the American Academy of Arts and Sciences in 1950 . In 1952 he was awarded the Max Planck Medal . In 1958 he was accepted into the Accademia Nazionale dei Lincei in Rome; in the same year the election as a member of the Leopoldina took place . In 1963 he became a member ( associé étranger ) of the Académie des sciences . The British Crown also awarded him the Order of Merit .

In his honor, the Dirac Medal (ICTP) is awarded to scientists for outstanding achievements, as well as the Dirac Medal (UNSW) and the Dirac Medal (IOP) . An asteroid is named after Paul Dirac .

He is buried in Tallahassee, but since November 1995 a stone in the floor of Westminster Abbey near Newton's grave, on which the Dirac equation is carved, has been commemorating him. The Dean of Westminster Abbey Michael Mayne had long resisted this because Dirac was an avowed atheist.

See also


  • The Principles of Quantum Mechanics , Oxford: Oxford University Press, 1958, ISBN 0-19-852011-5 (first 1930, from 3rd edition 1947 bra-ket notation, 4th edition 1957)
  • Lectures on quantum mechanics 1966
  • General Theory of Relativity , Princeton: Landmarks in Physics, 1996, ISBN 0-691-01146-X (first 1975)
  • Directions in physics , 1978 (Lectures Australia 1975)
  • Dalitz (Ed.) Collected Works of PAMDirac (1924–1938) , Cambridge 1996

Some essays:

  • Proceedings Royal Society , Volume 109, 1925, p. 642 (connection between classic Poisson brackets and quantum mechanical commutators)
  • Physical interpretation of quantum dynamics , Proceedings of the Royal Society , Volume 113, 1927, p. 621 (transformation theory, its general formulation of quantum mechanics)
  • On the theory of quantum mechanics , Proceedings of the Royal Society Volume 112, 1926, 661 (Fermi-Dirac and Bose statistics)
  • Quantum theory of emission and absorption of radiation (second quantization, fundamentals of quantum field theory)
  • The quantum theory of the electron (PDF) Proceedings or the Royal Society Volume 117, 1928, pp. 610-624, Volume 118, p. 351 (Dirac equation, spin)
  • A theory of electrons and positrons , Proceedings of the Royal Society, Volume 126, 1930, 360 (hole theory)
  • Quantized singularities of the electromagnetic field ( Memento from February 19, 2008 in the Internet Archive ), Proc. Roy. Soc. Volume 133, 1931, p. 60 (magnetic monopole, forecast positron)
  • Proceedings Cambridge Philosophical Society, Volume 35, 1939, p. 416 (for the first time bra-ket notation)
  • Proceedings Cambridge Philosophical Society, Volume 25, 1929, p. 62 (density matrix, less abstract than John von Neumann's )


  • Richard Dalitz , Rudolf Peierls : Paul Adrien Maurice Dirac, 8 August 1902–20 October 1984 . In: Biographical Memoirs of Fellows of the Royal Society of London 32. 1986, pp. 137-185
  • Helge Kragh : Dirac . Cambridge University Press, Cambridge 1990, ISBN 0-521-38089-8
  • Abraham Pais , Peter Goddard : Paul Dirac: the man and his work . Cambridge University Press, Cambridge 2005, ISBN 0-521-01953-2 .
  • Abdus Salam , Eugene Wigner (Eds.): Aspects of quantum theory . Cambridge University Press, Cambridge 1972, ISBN 0-521-08600-0 . (including: Eden, John Polkinghorne : Dirac in Cambridge . Van Vleck : Travels with Dirac in the Rockies . Jagdish Mehra The golden age of theoretical physics: Dirac's scientific work from 1924–1933 )
  • John Gerald Taylor: Tributes to Paul Dirac . A. Hilger, Bristol 1987, ISBN 0-85274-480-3 .
  • Graham Farmelo : The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius. Faber and Faber, London 2009, ISBN 978-0-571-22278-0 (he received the Kelvin Medal of the Institute of Physics in 2012, especially for his Dirac biography )
  • Howard Baer, ​​Alexander Belyaev (editors): Proceedings of the Dirac Centennial Symposium. University of Florida, Tallahassee 6-7 December 2002 , World Scientific 2003 (including Monica Dirac about her father)

Web links

Commons : Paul Dirac  - collection of images, videos and audio files



Individual evidence

  1. ^ PAM Dirac: The quantum theory of the electron . In: Proceedings or the Royal Society , Volume 117, 1928, p. 610, Volume 118, p. 351
  2. Dirac. In: Proc. Roy. Soc. , A, 126, 1929, p. 360. Nature , Volume 126, 1930, p. 605. Dirac later said that at that time it was generally assumed that the electron and proton were the only elementary particles. Robert Oppenheimer , Igor Tamm and Hermann Weyl criticized the identification as early as 1930 and Dirac also turned away from it in 1931 and postulated a new particle (Proc. Roy. Soc. A 133, 1931, p. 60). The name positron first appears in 1933 in a work by Carl Anderson (Physical Review, Volume 43, p. 491). Abraham Pais Paul Dirac. Aspects of his life and work , p. 15f, in Pais u. a. Paul Dirac , Cambridge University Press 1998
  3. ^ Proceedings or the Royal Society , A, Volume 133, p. 60. Physical Review , Volume 74, 1948, p. 817
  4. Nature , Volume 139, 1937, p. 323
  5. Proceedings Roal Society , Vol 167, 1938, pp 148
  6. Physical Journal of the Soviet Union , Volume 3, 1933, p. 64
  7. ^ Reviews of modern physics
  8. PAM Dirac: Is there an Aether? In: Nature , Volume 168, 1951, pp. 906-907.
  9. ^ PAM Dirac: The position of the ether in the physics . In: Naturwissenschaftliche Rundschau , 6, 1953, pp. 441–446
  10. ^ PAM Dirac: Quantum mechanics and the aether . In: The Scientific Monthly , 78, 1954, pp. 142-146
  11. ^ Proceedings Royal Society , A, Volume 268, p. 57
  12. 5997 Dirac (1983 TH9) JPL Small-Body Database Browser; 5997 Dirac en.wikipedia (Retrieved May 11, 2010)
  13. Westminster Abbey, Dirac
  14. Blog of Dirac biographer Graham Farmelo