Editing Quantum electrodynamics (section)

==History==
{{Main|History of quantum mechanics|History of quantum field theory}}
[[File:Dirac 3.jpg|upright|thumb|right|[[Paul Dirac]]]]

The first formulation of a [[quantum mechanics|quantum theory]] describing radiation and matter interaction is attributed to British scientist [[Paul Dirac]], who during the 1920s computed the coefficient of [[spontaneous emission]] of an [[atom]].<ref name=dirac>
{{cite journal
 | author=P. A. M. Dirac
 | author-link= Paul Dirac
 | year=1927
 | title=The Quantum Theory of the Emission and Absorption of Radiation
 | journal=[[Proceedings of the Royal Society of London A]]
 | volume=114 | pages=243–65
 | doi=10.1098/rspa.1927.0039
|bibcode = 1927RSPSA.114..243D
 | issue=767 | doi-access=free
}}</ref> He is credited with coining the term "quantum electrodynamics".<ref>{{Cite web |title=Quantum Field Theory > The History of QFT  |url=https://plato.stanford.edu/entries/quantum-field-theory/qft-history.html |access-date=2023-10-22 |website=Stanford Encyclopedia of Philosophy |first1=Meinard |last1=Kuhlmann |date=Aug 10, 2020 |orig-date=Jun 22, 2006 |url-status=live |archive-url=https://archive.today/20240616034116/https://plato.stanford.edu/entries/quantum-field-theory/qft-history.html |archive-date= 16 Jun 2024 }}</ref>

Dirac described the quantization of the [[electromagnetic field]] as an ensemble of [[harmonic oscillator]]s with the introduction of the concept of [[creation and annihilation operators]] of particles. In the following years, with contributions from [[Wolfgang Pauli]], [[Eugene Wigner]], [[Pascual Jordan]], [[Werner Heisenberg]] and [[Enrico Fermi]],<ref name="fermi">
{{cite journal
 | author=E. Fermi
 | author-link= Enrico Fermi
 | year=1932
 | title=Quantum Theory of Radiation
 | journal=[[Reviews of Modern Physics]]
 | volume=4 | issue= 1
 | pages=87–132
 | doi=10.1103/RevModPhys.4.87
|bibcode = 1932RvMP....4...87F }}</ref> physicists came to believe that, in principle, it was possible to perform any computation for any physical process involving photons and charged particles. However, further studies by [[Felix Bloch]] with [[Arnold Nordsieck]],<ref name="bloch">{{cite journal
 | author-link1= Felix Bloch
 | author-link2= Arnold Nordsieck
 | year=1937
 | title=Note on the Radiation Field of the Electron
 | journal=[[Physical Review]]
 | volume=52 | pages=54–59
 | doi=10.1103/PhysRev.52.54
|bibcode = 1937PhRv...52...54B
 | issue=2
 | last1= Bloch
 | first1= F.
 | last2= Nordsieck
 | first2= A.
}}</ref> and [[Victor Weisskopf]],<ref name=weisskopf>{{cite journal
 | author=V. F. Weisskopf
 | author-link= Victor Weisskopf
 | year=1939
 | title=On the Self-Energy and the Electromagnetic Field of the Electron
 | journal=[[Physical Review]]
 | volume=56 | issue= 1
 | pages=72–85
 | doi=10.1103/PhysRev.56.72
|bibcode = 1939PhRv...56...72W }}</ref>  in 1937 and 1939, revealed that such computations were reliable only at a first order of [[Perturbation theory (quantum mechanics)|perturbation theory]], a problem already pointed out by [[Robert Oppenheimer]].<ref name=oppenheimer>{{cite journal
 | author=R. Oppenheimer
 | author-link= J. Robert Oppenheimer
 | year=1930
 | title=Note on the Theory of the Interaction of Field and Matter
 | journal=[[Physical Review]]
 | volume=35 | pages=461–77
 | doi=10.1103/PhysRev.35.461
|bibcode = 1930PhRv...35..461O
 | issue=5 }}</ref> At higher orders in the series infinities emerged, making such computations meaningless and casting doubt on the theory's internal consistency. This suggested that [[special relativity]] and [[quantum mechanics]] were fundamentally incompatible.

[[File:Hans Bethe.jpg|upright|thumb|[[Hans Bethe]] ]]
Difficulties increased through the end of the 1940s. Improvements in [[microwave]] technology made it possible to take more precise measurements of the shift of the levels of a [[hydrogen atom]],<ref name=lamb>
{{cite journal
 | author-link1= Willis Lamb
 | author-link2=Robert Retherford
 | year=1947
 | title=Fine Structure of the Hydrogen Atom by a Microwave Method
 | journal=[[Physical Review]]
 | volume=72 | pages= 241–43
 | doi=10.1103/PhysRev.72.241
|bibcode = 1947PhRv...72..241L
 | issue=3
 | last1= Lamb
 | first1= Willis
 | last2= Retherford
 | first2= Robert
 | doi-access=free
 }}</ref> later known as the [[Lamb shift]] and [[magnetic moment]] of the electron.<ref name=foley>
{{cite journal
 | author-link2=Polykarp Kusch
 | author-link1=Henry M. Foley
 | year=1948
 | title=On the Intrinsic Moment of the Electron
 | journal=[[Physical Review]]
 | volume=73 | page=412
 | doi=10.1103/PhysRev.73.412
 | bibcode = 1948PhRv...73..412F
 | issue=3
 | last1= Foley
 | first1= H.M.
 | last2= Kusch
 | first2= P. }}</ref> These experiments exposed discrepancies that the theory was unable to explain.

A first indication of a possible solution was given by Bethe in 1947.<ref name=bethe/><ref name=schweber>
{{cite book
 | last=Schweber
 | first=Silvan
 | author-link=Silvan Schweber
 | year=1994
 | isbn=978-0-691-03327-3
 | title=QED and the Men Who Did it: Dyson, Feynman, Schwinger, and Tomonaga
 | chapter=Chapter 5
 | page=[https://archive.org/details/qedmenwhomadeitd0000schw/page/230 230]
 | publisher=Princeton University Press
 | chapter-url=https://archive.org/details/qedmenwhomadeitd0000schw/page/230
 }}</ref>  He made the first non-relativistic computation of the shift of the lines of the hydrogen atom as measured by Lamb and [[Robert Retherford|Retherford]].<ref name=bethe>
{{cite journal
 | author=H. Bethe
 | author-link= Hans Bethe
 | year=1947
 | title=The Electromagnetic Shift of Energy Levels
 | journal=[[Physical Review]]
 | volume=72 | pages=339–41
 | doi=10.1103/PhysRev.72.339
|bibcode = 1947PhRv...72..339B
 | issue=4 | s2cid= 120434909
 }}</ref> Despite limitations of the computation, agreement was excellent. The idea was simply to attach infinities to corrections of [[mass]] and [[charge (physics)|charge]] that were actually fixed to a finite value by experiments. In this way, the infinities get absorbed in those constants and yield a finite result with good experimental agreement. This procedure was named [[renormalization]].

[[File:Feynman and Oppenheimer at Los Alamos.jpg|thumb|right|[[Richard Feynman|Feynman]] (center) and [[J. Robert Oppenheimer|Oppenheimer]] (right) at [[Los Alamos National Laboratory|Los Alamos]].]]

Based on Bethe's intuition and fundamental papers on the subject by [[Shin'ichirō Tomonaga]],<ref name=tomonaga>
{{cite journal
 | author=S. Tomonaga
 | author-link= Sin-Itiro Tomonaga
 | year=1946
 | title=On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields
 | journal=[[Progress of Theoretical Physics]]
 | volume=1 | pages= 27–42
 | doi=10.1143/PTP.1.27
 | issue=2
| bibcode=1946PThPh...1...27T
 | doi-access=free
 }}</ref> [[Julian Schwinger]],<ref name=schwinger1>
{{cite journal
 | author=J. Schwinger
 | author-link= Julian Schwinger
 | year=1948
 | title=On Quantum-Electrodynamics and the Magnetic Moment of the Electron
 | journal=[[Physical Review]]
 | volume=73 | pages= 416–17
 | doi=10.1103/PhysRev.73.416
|bibcode = 1948PhRv...73..416S
 | issue=4 | doi-access=free
 }}</ref><ref name=schwinger2>
{{cite journal
 | author=J. Schwinger
 | author-link= Julian Schwinger
 | year=1948
 | title=Quantum Electrodynamics. I. A Covariant Formulation
 | journal=[[Physical Review]]
 | volume=74 | pages= 1439–61
 | doi=10.1103/PhysRev.74.1439
|bibcode = 1948PhRv...74.1439S
 | issue=10 }}</ref> [[Richard Feynman]]<ref name=feynman1>
{{cite journal
 | author=R. P. Feynman
 | author-link= Richard Feynman
 | year=1949
 | title=Space–Time Approach to Quantum Electrodynamics
 | journal=[[Physical Review]]
 | volume=76 | pages= 769–89
 | doi=10.1103/PhysRev.76.769
|bibcode = 1949PhRv...76..769F
 | issue=6 | doi-access=free
 }}</ref><ref name=feynman2>{{cite journal
 |author       = R. P. Feynman
 |author-link  = Richard Feynman
 |year         = 1949
 |title        = The Theory of Positrons
 |journal      = [[Physical Review]]
 |volume       = 76
 |pages        = 749–59
 |doi          = 10.1103/PhysRev.76.749
 |bibcode      = 1949PhRv...76..749F
 |issue        = 6
 |s2cid        = 120117564
 |url          = https://authors.library.caltech.edu/3520/
 |access-date  = 2021-11-19
 |archive-date = 2022-08-09
 |archive-url  = https://web.archive.org/web/20220809030941/https://authors.library.caltech.edu/3520/
 |url-status   = dead
|url-access= subscription
 }}</ref><ref name=feynman3>
{{cite journal
 | author=R. P. Feynman
 | author-link= Richard Feynman
 | year=1950
 | title=Mathematical Formulation of the Quantum Theory of Electromagnetic Interaction
 | journal=[[Physical Review]]
 | volume=80 | pages= 440–57
 | doi=10.1103/PhysRev.80.440
|bibcode = 1950PhRv...80..440F
 | issue=3 | url=https://authors.library.caltech.edu/3528/1/FEYpr50.pdf
 }}</ref> and [[Freeman Dyson]],<ref name=dyson1>
{{cite journal
 | author=F. Dyson
 | author-link= Freeman Dyson
 | year=1949
 | title=The Radiation Theories of Tomonaga, Schwinger, and Feynman
 | journal=[[Physical Review]]
 | volume=75 | pages= 486–502
 | doi=10.1103/PhysRev.75.486
|bibcode = 1949PhRv...75..486D
 | issue=3 | doi-access=free
 }}</ref><ref name=dyson2>
{{cite journal
 | author=F. Dyson
 | author-link= Freeman Dyson
 | year=1949
 | title=The S Matrix in Quantum Electrodynamics
 | journal=[[Physical Review]]
 | volume=75 | pages=  1736–55
 | doi=10.1103/PhysRev.75.1736
|bibcode = 1949PhRv...75.1736D
 | issue=11 }}</ref> it was finally possible to produce fully [[Lorentz covariance|covariant]] formulations that were finite at any order in a perturbation series of quantum electrodynamics. Tomonaga, Schwinger, and Feynman were jointly awarded the 1965 [[Nobel Prize in Physics]] for their work in this area.<ref name=nobel65>{{cite web | title = The Nobel Prize in Physics 1965 | publisher = Nobel Foundation | url = http://nobelprize.org/nobel_prizes/physics/laureates/1965/index.html|access-date=2008-10-09}}</ref> Their contributions, and Dyson's, were about [[Lorentz covariance|covariant]] and [[gauge-invariant]] formulations of quantum electrodynamics that allow computations of observables at any order of [[Perturbation theory (quantum mechanics)|perturbation theory]]. Feynman's mathematical technique, based on his [[Feynman diagram|diagrams]], initially seemed unlike the field-theoretic, [[Operator (physics)|operator]]-based approach of Schwinger and Tomonaga, but Dyson later showed that the two approaches were equivalent.<ref name="dyson1"/> Renormalization, the need to attach a physical meaning at certain divergences appearing in the theory through [[integral]]s, became one of the fundamental aspects of [[quantum field theory]] and is seen as a criterion for a theory's general acceptability. Even though renormalization works well in practice, Feynman was never entirely comfortable with its mathematical validity, referring to renormalization as a "shell game" and "hocus pocus".<ref name=feynbook/>{{rp|128}}

Neither Feynman nor Dirac were happy with that way to approach the observations made in theoretical physics, above all in quantum mechanics.<ref name=":1">{{Citation |title=The story of the positron - Paul Dirac (1975) |url=https://www.youtube.com/watch?v=Ci86Aps7CMo |access-date=2023-07-19 |language=en}}</ref>

QED is the model and template for all subsequent quantum field theories. One such subsequent theory is [[quantum chromodynamics]], which began in the early 1960s and attained its present form in the 1970s, developed by [[H. David Politzer]], [[Sidney Coleman]], [[David Gross]] and [[Frank Wilczek]]. Building on Schwinger's pioneering work, [[Gerald Guralnik]], [[C. R. Hagen|Dick Hagen]], and [[Tom W. B. Kibble|Tom Kibble]],<ref>
{{cite journal
 | last1=Guralnik | first1=G. S.
 | last2=Hagen | first2=C. R.
 | last3=Kibble | first3=T. W. B.
 | year=1964
 | title=Global Conservation Laws and Massless Particles
 | journal=[[Physical Review Letters]]
 | volume=13 | pages=585–87
 | doi=10.1103/PhysRevLett.13.585
 | bibcode = 1964PhRvL..13..585G
 | issue=20 | doi-access=free
 }}</ref><ref>
{{cite journal
 | last=Guralnik
 | first=G. S.
 | year=2009
 | title=The History of the Guralnik, Hagen and Kibble development of the Theory of Spontaneous Symmetry Breaking and Gauge Particles
 | journal=[[International Journal of Modern Physics A]]
 | volume=24 | pages=2601–27
 | doi=10.1142/S0217751X09045431
 | arxiv=0907.3466
|bibcode = 2009IJMPA..24.2601G
 | issue=14 | s2cid=16298371
 }}</ref> [[Peter Higgs]], [[Jeffrey Goldstone]], and others, [[Sheldon Glashow]], [[Steven Weinberg]] and [[Abdus Salam]] independently showed how the [[weak nuclear force]] and quantum electrodynamics could be merged into a single [[electroweak force]].