Editing Paul Dirac (section)

===The Dirac equation===
{{further|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 (physics)|spin]] systems (Dirac told [[Abraham Pais]], "I believe I got these [matrices] independently of Pauli and possibly Pauli got these independently of me."),<ref>{{cite book|title=Reminiscences about a Great Physicist|publisher=Cambridge University Press|page=[https://books.google.com/books?id=1Pg7t9a_AX4C&pg=PA98 98]|editor1=Behram N. Kurşunoğlu |editor2=Eugene Paul Wigner }}</ref> he proposed the [[Dirac equation]] as a [[Special relativity|relativistic]] [[equation of motion]] for the [[wave function]] of the [[electron]].<ref>{{cite journal |last=Dirac |first=P. A. M. |title=The Quantum Theory of the Electron  |journal=Proceedings of the Royal Society of London A |date=1 February 1928 |volume=117 |issue=778 |pages=610–24 |doi=10.1098/rspa.1928.0023 |bibcode=1928RSPSA.117..610D|doi-access=free }}</ref> 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]]''.<ref>{{Nobelprize}} with his Nobel Lecture, 12 December 1933 ''Theory of Electrons and Positrons''</ref> The positron was observed by [[Carl David Anderson|Carl Anderson]] in 1932. Dirac's equation also contributed to explaining the origin of [[Spin (physics)|quantum spin]] as a relativistic phenomenon.

The necessity of [[fermion]]s (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 ''[[Planck constant|ħ]]''/2, itself subject to quantisation conditions involving [[Anticommutativity|anti-commutators]]. Thus reinterpreted, in 1934 by [[Werner Heisenberg]], as a (quantum) field equation accurately describing all elementary matter particles – today [[quark]]s and [[lepton]]s – this [[Dirac field]] equation is as central to theoretical physics as the [[Maxwell equations|Maxwell]], [[Yang–Mills theory|Yang–Mills]] and [[General relativity|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 [[Julian Schwinger|Schwinger]], [[Richard Feynman|Feynman]], [[Sin-Itiro Tomonaga]] and [[Freeman Dyson|Dyson]] in their formulation of quantum electrodynamics.

Dirac's [[The Principles of Quantum Mechanics|''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 Schrödinger]] on [[Schrödinger equation|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 [[Dirac delta function]]. Following his 1939 article,<ref>{{cite journal|author=P. A. M. Dirac |year=1939 |title=A New Notation for Quantum Mechanics |journal=Proceedings of the Cambridge Philosophical Society |volume=35 |issue=3 |page=416 |doi=10.1017/S0305004100021162 |bibcode=1939PCPS...35..416D|s2cid=121466183 }}</ref> he also included the [[bra–ket notation]] in the third edition of his book,<ref>{{cite journal |author1=Gieres |doi=10.1088/0034-4885/63/12/201 |title=Mathematical surprises and Dirac's formalism in quantum mechanics |year=2000 |volume=63 |issue=12 |page=1893 |journal=Reports on Progress in Physics |arxiv=quant-ph/9907069 |bibcode = 2000RPPh...63.1893G|s2cid=10854218 }}</ref> thereby contributing to its universal use nowadays.