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{{Short description|American physicist (1922–2013)}}
{{Use mdy dates|date=September 2021}}
{{Infobox scientist
| name = Arthur Strong Wightman
| birth_date = {{Birth date|1922|3|30|mf=y}}
| birth_place = [[Rochester, New York]]
| death_date = {{Death date and age|2013|1|13|1922|3|30}}<ref name=obit/>
| death_place = [[Edison, New Jersey]]
| nationality = [[United States|U.S.]]
| field = [[Physics]]
| work_institution = {{Unbulleted list|[[Yale University]] {{smaller|(1943-44){{nbsp|2}}}}|[[Princeton University]] {{smaller|(1949-71){{nbsp|2}}}}}}
| alma_mater = {{Unbulleted list|[[Yale University]] {{smaller|(B.A., 1942){{nbsp|2}}}}|[[Princeton University]] {{smaller|(Ph.D, 1949){{nbsp|2}}}}}}
| doctoral_advisor = [[John Archibald Wheeler]]
| thesis_title = The Moderation and Absorption of Negative Pions in Hydrogen
| thesis_url = https://ui.adsabs.harvard.edu/abs/1949PhDT........16W/abstract
| thesis_year = 1949
| doctoral_students = {{Unbulleted list|[[Lawrence Schulman]]|[[Huzihiro Araki]]|[[Richard Allan Ferrell|Richard Ferrell]]|[[Stephen Fulling]]|[[Arthur Jaffe]]|[[Oscar Lanford]]|[[Jerrold Marsden]]|[[Eduard Prugovecki]]|[[Silvan S. Schweber]]|[[Barry Simon]]|[[Alan Sokal]]}}
| known_for = {{Unbulleted list|[[Axiomatic quantum field theory]]|[[Superselection]]|[[Wightman axioms]]}}
| prizes = {{Unbulleted list|[[Dannie Heineman Prize for Mathematical Physics|Heineman Prize]] {{smaller|(1969){{nbsp|2}}}}|[[Henri Poincaré Prize]] {{smaller|(1997){{nbsp|2}}}}}}
}}
'''Arthur Strong Wightman''' (March 30, 1922 – January 13, 2013) was an American mathematical [[physicist]]. He was one of the founders of the axiomatic approach to [[quantum field theory]], and originated the set of [[Wightman axioms]].<ref name=obit>{{cite web|last=Kelly |first=Morgan |url=http://www.princeton.edu/main/news/archive/S35/94/19A97/index.xml?section=topstories |title=Princeton University - Esteemed Princeton mathematical physicist and mentor Arthur Wightman dies |publisher=Princeton.edu |date=January 30, 2013 |access-date=February 13, 2013}}</ref> With his rigorous treatment of quantum field theories, he promoted research on various aspects of modern [[mathematical physics]].<ref name=HP_citation>{{cite web|url=http://www.iamp.org/poincare/aw97-cit.html|website=International Association of Mathematical Physics|title=Wightman's Henri Poincaré Prize citation|access-date=March 9, 2021}}</ref>

== Biography ==
Arthur Wightman was born on March 30, 1922, in [[Rochester, New York|Rochester]], in [[New York (state)|New York]]. He studied at the [[Yale University]] and in 1942 he earned a bachelor's degree in physics. In 1949 he received his doctorate at the [[Princeton University]] under the supervision of [[John Archibald Wheeler|John Wheeler]].<ref>The doctoral thesis is {{cite thesis|last=Wightman|first=Arthur|date=1949|title=The Moderation and Absorption of Negative Pions in Hydrogen|bibcode=1949PhDT........16W|url=https://ui.adsabs.harvard.edu/abs/1949PhDT........16W/abstract|place=Princeton}}</ref> He intended to graduate with [[Eugene Wigner]], but he was spending most of his time at the [[Oak Ridge National Laboratory]].<ref>{{cite journal|editor=Simon, Barry|editor-link=Barry Simon|title=In Memory of Arthur Strong Wightman|journal=Notices of the AMS|date=March 2015|volume=62|issue=3|pages=249–257|doi=10.1090/noti1219|url=https://www.ams.org/notices/201503/rnoti-p249.pdf|doi-access=free}}</ref> In the early 1950s, he started as a young instructor in the Princeton Physics department and later became the Thomas D. Jones Professor of Mathematical Physics, in 1971. He retired in 1992 as [[professor emeritus]].<ref>{{cite web|last1=Aizenman|first1=Michael|last2=Lieb|first2=Elliott|last3=Nelson|first3=Edward|url=https://phy.princeton.edu/department/history/faculty-history/arthur-wightman|website=Princeton University|title=Arthur Strong Wightman 1922-2013|access-date=March 9, 2021}}</ref> In the years 1951–1952 and 1956–1957 he was a visiting researcher at the [[University of Copenhagen]] at the [[Niels Bohr Institute]], where he worked in particular with [[Gunnar Källén]] and [[Lars Gårding]]. In 1957 he was at the [[University of Paris]] and in the years 1963–1964 and 1968–1969 at the [[Institut des Hautes Études Scientifiques]]. Between 1977 and 1978 he was [[visiting professor]] at the {{lang|fr|[[École Polytechnique]]|italic=no}} in [[Paris]] and in 1982 at the [[University of Adelaide]].<ref>{{cite web|url=https://www.aip.org/history/acap/biographies/bio.jsp?wightmana|archive-url=https://web.archive.org/web/20151222231720/https://www.aip.org/history/acap/biographies/bio.jsp?wightmana|title=Biography from the APS|website=aip.org|archive-date=December 22, 2015}}</ref>

Wightman has been married twice. His first wife, Anna-Greta Larsson, was an artist and photographer and died early. They had a daughter, Robin, who also died prematurely. The second wife was the Bulgarian translator Ludmilla Popova Wightman. Wightman died on January 13, 2013, in [[Princeton, New Jersey|Princeton]], in [[New Jersey]].<ref name=IAMP_Bulletin>{{Cite journal|last1=Jaffe|first1=Arthur|last2=Simon|first2=Barry|title=Arthur Strong Wightman (1922–2013)|journal=News Bulletin, International Association of Mathematical Physics|pages=34–36|date=January 2013|url=http://math.caltech.edu/SimonPapers/R57.pdf}}</ref>

== Scientific career ==
Already during his undergraduate studies, Arthur Wightman had close contacts with the mathematics department in Princeton. Together with the mathematician [[John Tate (mathematician)|John Tate]], Wightman was engaged in the work on the Lorentz and [[Representation theory of the Poincaré group|Poincaré groups representations]].<ref>{{Cite journal|last1=Jaffe|first1=Arthur|last2=Wightman|first2=Arthur S.|last3=Jost|first3=Res|title=For Res Jost, and To Arthur Wightman|journal=Communications in Mathematical Physics|volume=132|number=1|pages=1–4|year=1990|doi=10.1007/BF02277996|url=https://projecteuclid.org/euclid.cmp/1104201026}}</ref>

In the 1950s, he introduced his [[Wightman axioms]] as a mathematical foundation to relativistic quantum field theory. Quantum fields are treated as [[distribution (mathematics)|distributions]] in space-time. The [[Hilbert space]] carries a unitary representation of the Poincaré group under which the field operators transform covariantly. Wightman's paper with D. Hall reported to a theorem that stated that the expectation value of the product of two fields, <math>\phi(x)\phi(y)</math>, could be [[analytical continuation| analytically continued]] to all separations <math>(x-y)</math>.<ref name=DuckSudarshanBook>{{Cite book |last=Duck |first=Ian |title=Pauli and the spin-statistics theorem |last2=Sudarshan |first2=Ennackel Chandy George |last3=Sudarshan |first3=E. C. G. |date=1998 |publisher=World Scientific |isbn=978-981-02-3114-9 |edition=1. reprint |location=Singapore}}</ref>{{rp|425}} Using this, [[Res Jost]] was able to derive the [[PCT theorem|PCT]] and the [[spin-statistics theorem]]s, as shown in Wightman's and [[Ray Streater|Streater]]'s book.<ref>{{Cite book|last1=Streater|first1=Raymond F.|last2=Wightman|first2=Arthur S.|date=1989|title=PCT, spin and statistics, and all that|isbn=978-0691070629}}</ref> Together with Eugene Wigner and [[Gian-Carlo Wick]], he introduced [[superselection|superselection rules]] and studied the representations of commutator and anti-commutator algebras with the mathematician [[Lars Gårding]].<ref>{{cite web|first=Ray|last=Streater|url=http://www.mth.kcl.ac.uk/~streater/PCT.html|archive-url=https://web.archive.org/web/20120716210613/http://www.mth.kcl.ac.uk/~streater/PCT.html|title=Table of contents, Streater, Wightman ''PCT, Spin, Statistics and all that''|website=mth.kcl.ac.uk|archive-date=July 16, 2012}}</ref>

== Honors and awards ==
In 1969 Arthur Wightman was awarded the [[Dannie Heineman Prize for Mathematical Physics]] for founding and contributing in developing axiomatic quantum field theory<ref>{{cite web|url=https://www.aps.org/programs/honors/prizes/prizerecipient.cfm?first_nm=Arthur&last_nm=Wightman&year=1969|title=1969 Dannie Heineman Prize for Mathematical Physics Recipient|website=American Physical Society|access-date=March 9, 2021}}</ref> and in 1997 the [[Henri Poincaré Prize]] of the [[International Association of Mathematical Physics]]<ref>{{cite web|url=http://www.iamp.org/page.php?page=page_prize_poincare|title=Henri Poincaré Prize winners|website=International Association of Mathematical Physics|access-date=March 9, 2021}}</ref> for his central role in the foundations of the general theory of quantum fields.<ref name=HP_citation /> Since 1964 he was a fellow of the [[American Physical Society]],<ref>{{cite web|url=https://www.aps.org/programs/honors/fellowships/archive-all.cfm?initial=W&year=1964|title=APS Fellow Archive|website=American Physical Society|access-date=March 9, 2021}}</ref> since 1966 of the [[American Academy of Arts and Sciences]],<ref>{{cite web|url=https://www.amacad.org/person/arthur-strong-wightman|title=American Academy of Arts and Sciences member page of Arthur Wightman|website=National Academy of Sciences|access-date=March 9, 2021}}</ref> and since 1970 of the [[United States National Academy of Sciences]].<ref>{{cite web|url=http://www.nasonline.org/member-directory/deceased-members/49130.html|title=National Academy of Sciences member page of Arthur Wightman|website=National Academy of Sciences|access-date=March 6, 2021}}</ref> In 1962 he was an invited speaker at the [[International Congress of Mathematicians]] in [[Stockholm]].<ref>{{cite web|url=https://www.mathunion.org/fileadmin/ICM/Proceedings/ICM1962.4/ICM1962.4.ocr.pdf|title=International Congress of Mathematicians. List of Members, Stockholm 1962|website=International Mathematical Union|access-date=March 9, 2021}}</ref> In 1976 he was [[Josiah Willard Gibbs Lectureship|Josiah Willard Gibbs Lecturer]].<ref>{{cite web|url=https://www.ams.org/meetings/lectures/meet-gibbs-lect|title=Josiah Willard Gibbs Lectures|website=American Mathematical Society|access-date=March 9, 2021}}</ref>

== Selected publications ==
{{div col|colwidth=35em}}
* {{Cite book|last1=Streater|first1=Raymond F.|last2=Wightman|first2=Arthur S.|date=1989|title=PCT, spin and statistics, and all that|isbn=978-0691070629}}
* {{Cite journal|last = Wightman|first = Arthur S.|title = Quantum Field Theory in Terms of Vacuum Expectation Values|journal = Physical Review|volume = 101|pages = 860–866|year = 1956|issue = 2|doi = 10.1103/PhysRev.101.860|bibcode = 1956PhRv..101..860W}} 
* {{Cite journal|last1 = Wightman|first1 = Arthur S.|last2=Gårding|first2=Lars|title = Fields as operator-valued distributions in relativistic quantum theory|journal = Arkiv för Fysik|volume = 28|year = 1965}}
* {{Cite journal|last=Wightman|first=Arthur S.|title=What is the point of so-called axiomatic field theory?|journal=Physics Today|volume=22|number=9|pages=53–58|year=1969|doi=10.1063/1.3035782|bibcode=1969PhT....22i..53W}} 
* {{Cite book|last=Wightman|first=Arthur S.|date=1967|title=Introduction to some aspects of the relativistic dynamics of quantized fields, Cargese Lectures in Theoretical Physics|publisher=Gordon and Breach Science Publishers}}
* {{Cite book|last=Wightman|first=Arthur S.|date=1977|chapter=Should We Believe in Quantum Field Theory?|title=15th Erice School of Subnuclear Physics: The Why's of Subnuclear Physics|pages=983–1025}}
* {{Cite journal|last1=Wick|first1=Gian Carlo|last2=Wightman|first2=Arthur S.|last3=Wigner|first3=Eugene P.|title=The intrinsic parity of elementary particles|journal=Physical Review|volume=88|pages=101–105|year=1952|issue=1|doi=10.1103/PhysRev.88.101|bibcode=1952PhRv...88..101W}}
* {{Cite journal|last=Wightman|first=Arthur S.|title=Looking back at quantum field theory|journal=Physica Scripta|volume=24|pages=813–816|year=1981|issue=5|doi=10.1088/0031-8949/24/5/001}}
* {{Cite journal|last1=Jaffe|first1=Arthur|last2=Wightman|first2=Arthur S.|last3=Jost|first3=Res|title=For Res Jost, and To Arthur Wightman|journal=Communications in Mathematical Physics|volume=132|number=1|pages=1–4|year=1990|doi=10.1007/BF02277996|url=https://projecteuclid.org/euclid.cmp/1104201026}}
* {{Cite journal|last=Wightman|first=Arthur S.|title=The theory of quantized fields in the 50s|journal=Pions to Quarks: Particle Physics in the 50s|volume=50|pages=255–261|year=1989}}
{{div col end}}

== See also ==
{{Portal|Physics|Biography}}
{{cols|colwidth=21em}}
* [[Axiomatic quantum field theory]]
* [[Hilbert's sixth problem]]
* [[PCT Theorem]]
* [[Principle of locality]]
* [[Quantum field theory]]
* [[Wightman axioms]]
* [[Borchers algebra|Wightman functional]]
{{colend}}

== References ==
{{reflist}}

== Further reading ==
* {{cite journal|editor=Simon, Barry|editor-link=Barry Simon|title=In Memory of Arthur Strong Wightman|journal=Notices of the AMS|date=March 2015|volume=62|issue=3|pages=249–257|doi=10.1090/noti1219|url=https://www.ams.org/notices/201503/rnoti-p249.pdf|doi-access=free}}
* {{cite web|last=Kelly|first=Morgan|url=http://www.princeton.edu/main/news/archive/S35/94/19A97/index.xml?section=topstories|title=Esteemed Princeton mathematical physicist and mentor Arthur Wightman dies|website=Princeton University|date=January 30, 2013|access-date=March 10, 2021}}
* {{cite web|last1=Aizenman|first1=Michael|last2=Lieb|first2=Elliott|last3=Nelson|first3=Edward|url=https://phy.princeton.edu/department/history/faculty-history/arthur-wightman|website=Princeton University|title=Arthur Strong Wightman 1922-2013|access-date=March 9, 2021}}
* {{Cite journal|last1=Jaffe|first1=Arthur|last2=Simon|first2=Barry|title=Arthur Strong Wightman (1922–2013)|journal=News Bulletin, International Association of Mathematical Physics|pages=34–36|date=January 2013|url=http://math.caltech.edu/SimonPapers/R57.pdf}}

== External links ==
{{wikiquote}}
* {{MathGenealogy|id=11904|title=Arthur Wightman}}.
* {{DNB-Portal|1057560499}}.
* {{zbMATH|id=wightman.arthur-s}}.
* {{cite web|first=Ray|last=Streater|url=http://www.mth.kcl.ac.uk/~streater/wightman.html|archive-url=https://web.archive.org/web/20030819031511/http://www.mth.kcl.ac.uk/~streater/wightman.html|title=Remarks with photo|website=mth.kcl.ac.uk|archive-date=August 19, 2003}}
* {{cite web|first=Ray|last=Streater|url=http://www.mth.kcl.ac.uk/~streater/PCT.html|archive-url=https://web.archive.org/web/20120716210613/http://www.mth.kcl.ac.uk/~streater/PCT.html|title=Table of contents, Streater, Wightman ''PCT, Spin, Statistics and all that''|website=mth.kcl.ac.uk|archive-date=July 16, 2012}}
* {{cite web|url=https://www.aip.org/history/acap/biographies/bio.jsp?wightmana|archive-url=https://web.archive.org/web/20151222231720/https://www.aip.org/history/acap/biographies/bio.jsp?wightmana|title=Biography from the APS|website=aip.org|archive-date=December 22, 2015}}
* {{cite web|url=http://www.iamp.org/poincare/aw97-cit.html|website=International Association of Mathematical Physics|title=Wightman's Henri Poincaré Prize citation|access-date=March 9, 2021}}

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{{DEFAULTSORT:Wightman, Arthur}}
[[Category:1922 births]]
[[Category:2013 deaths]]
[[Category:Scientists from Rochester, New York]]
[[Category:Fellows of the American Physical Society]]
[[Category:Members of the United States National Academy of Sciences]]
[[Category:American mathematical physicists]]
[[Category:Princeton University alumni]]
[[Category:Scientists from New York (state)]]
[[Category:Yale College alumni]]