Editing Paul Dirac (section)

===Quantum electrodynamics===
Dirac's [[quantum electrodynamics]] (QED) included terms with infinite [[self-energy]]. 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!"<ref>{{harvnb|Kragh|1990|p=184}}</ref> His refusal to accept [[renormalisation]] resulted in his work on the subject moving increasingly out of the mainstream. [[Shin'ichirō Tomonaga]], [[Julian Schwinger|Schwinger]] and [[Richard Feynman|Feynman]] mastered this approach, producing a QED with unprecedented accuracy, resulting formal recognition by an award of the Nobel Prize for physics.<ref>{{harvnb|Schweber|1994}}</ref>

In the 1950s in his search for a better QED, Paul Dirac developed the Hamiltonian theory of constraints<ref>{{Cite journal |last=Dirac |first=P. a. M. |date=1950 |title=Generalized Hamiltonian Dynamics |url=https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/generalized-hamiltonian-dynamics/F4C30A59B59BEE09E9CB6F07377B8BD3 |journal=Canadian Journal of Mathematics |language=en |volume=2 |pages=129–148 |doi=10.4153/CJM-1950-012-1 |issn=0008-414X}}</ref><ref>{{Cite journal |last=Dirac |first=P. a. M. |date=1951 |title=The Hamiltonian Form of Field Dynamics |url=https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/hamiltonian-form-of-field-dynamics/E17F213F85E3377BC2EBB3A1E0876BC8 |journal=Canadian Journal of Mathematics |language=en |volume=3 |pages=1–23 |doi=10.4153/CJM-1951-001-2 |issn=0008-414X}}</ref> based{{citation needed|date=July 2024}} on lectures that he delivered at the 1949 [[International Congress of Mathematicians|International Mathematical Congress]] in Canada. Dirac had also solved the problem of putting the [[Schwinger–Tomonaga equation]] into the Schrödinger representation<ref>Phillips R. J. N. 1987 ''Tributes to Dirac'' p31 London: Adam Hilger</ref> and given explicit expressions for the [[Scalar field|scalar meson field]] ([[pion|spin zero pion]] or [[pseudoscalar meson]]), the vector meson field (spin one rho meson), and the electromagnetic field (spin one massless boson, photon).