Paul Adrien Maurice Dirac (1902-1984)
Introducing the idea into quantum mechanics that came to be known as canonical quantization (the deformation of Poisson brackets into commutators of linear operators):
Early discussion of the foundations of quantum mechanics (including the possibly first consideration of what came to be known as the Slater determinant):
and with early emphasis of the Born-Pauli rule:
Introducing what came to be called Dirac charge quantization (flux quantization) of the electromagnetic field and its potential magnetic monopole sources:
Precursor discussion to the path integral-formulation of quantum mechanics:
Introducing bra-ket-notation to quantum mechanics:
Introducing the modern theory of constrained Hamiltonian mechanics:
Paul A. M. Dirac, Generalized Hamiltonian Dynamics, Canadian Journal of Mathematics 2 (1950) 129-148 [doi:10.4153/CJM-1950-012-1]
reprinted in:
Alexander S. Blum, Dean Rickles (eds.), Ch.34 in: Quantum Gravity in the First Half of the Twentieth Century: A Sourcebook, Edition Open Sources 10 (2018) 484-503 [doi:10.34663/9783945561317-00, pdf]
On a relativistic membrane model for the electron:
Paul Dirac, An Extensible Model of the Electron, Proc. Roy. Soc. A 268 (1962) 57-67 [jstor:2414316]
(also proposing the Dirac-Born-Infeld action)
Paul Dirac, The motion of an Extended Particle in the Gravitational Field, in: L. Infeld (ed.), Relativistic Theories of Gravitation, Proceedings of a Conference held in Warsaw and Jablonna, July 1962, P. W. N. Publishers, 1964, Warsaw, 163-171; discussion 171-175 [spire:1623740, article:pdf, full proceedings:pdf]
Paul Dirac, Particles of Finite Size in the Gravitational Field, Proc. Roy. Soc. A 270 (1962) 354-356 [doi:10.1098/rspa.1962.0228]
On quantum mechanics (and some quantum field theory):
Paul Dirac, The Principles of Quantum Mechanics, International series of monographs on physics, Oxford University Press (1930) [ISBN:9780198520115]
Paul Dirac, The mathematical foundations of quantum theory, pages 1-8 in A. R. Marlow (ed.) Mathematical Foundations of Quantum Theory, Ac. Press 1978
Early discussion of the positron:
Personal reminiscences of the early history of special relativity and quantum mechanics:
On syntax:
[Dirac 1939] In mathematical theories the question of notation, while not of primary importance, is yet worthy of careful consideration, since a good notation can be of great value in helping the development of a theory, by making it easy to write down those quantities or combinations of quantities that are important, and difficult or impossible to write down those that are unimportant.
[Dirac 1978:] One should keep the need for a sound mathematical basis dominating one’s search for a new theory. Any physical or philosophical ideas that one has must be adjusted to fit the mathematics. Not the way round.
Too many physicists are inclined to start from some preconceived physical ideas and then to try to develop them and find a mathematical scheme that incorporates them. Such a line of attack is unlikely to lead to success. One runs into difficulties and finds no reasonable way out of them. One ought then to realize that one’s whole line of approach is wrong and to seek a new starting point with a sound mathematical basis.
On anxiety with new ideas:
I think he [Heisenberg] failed to make this discovery simply because he was too scared. He was afraid of his own bold new idea, and he was afraid that if he went too far with it, it might all break down.
I had a great advantage over Heisenberg. I did not have any of these fears, because it was not my idea. I could play about with this non-commuting algebra… and see where it led
(Similar comments are in Dirac 1977)
Last revised on January 27, 2026 at 16:54:25. See the history of this page for a list of all contributions to it.