Arthur Wightman

Arthur Strong Wightman (March 30, 1922 – January

13, 2013) was an American mathematical physicist. He Arthur Strong Wightman
was one of the founders of the axiomatic approach to Born March 30, 1922
quantum field theory, and originated the set of Rochester, New York
Wightman axioms.[1] With his rigorous treatment of Died January 13, 2013 (aged 90)[1]
quantum field theories, he promoted research on Edison, New Jersey
various aspects of modern mathematical physics.[2] Nationality U.S.
Alma mater Yale University (B.A., 1942)

Biography Princeton University (Ph.D, 1949)

Known for Axiomatic quantum field theory

Arthur Wightman was born on March 30, 1922, in
Superselection
Rochester, in New York. He studied at the Yale
University and in 1942 he earned a bachelor's degree Wightman axioms
in physics. In 1949 he received his doctorate at the Awards Heineman Prize (1969)
Princeton University under the supervision of John Henri Poincaré Prize (1997)
Wheeler.[3] He intended to graduate with Eugene
Wigner, but he was spending most of his time at the Scientific career
Oak Ridge National Laboratory.[4] In the early 1950s, Fields Physics
he started as a young instructor in the Princeton Institutions Yale University (1943-44)
Physics department and later became the Thomas D.
Princeton University (1949-71)
Jones Professor of Mathematical Physics, in 1971. He
retired in 1992 as professor emeritus.[5] In the years Thesis The Moderation and Absorption
1951–1952 and 1956–1957 he was a visiting of Negative Pions in Hydrogen
researcher at the University of Copenhagen at the Niels (https://ui.adsabs.harvard.edu/ab
Bohr Institute, where he worked in particular with s/1949PhDT........16W/abstrac
Gunnar Källén and Lars Gårding. In 1957 he was at the t) (1949)
University of Paris and in the years 1963–1964 and Doctoral John Archibald Wheeler
1968–1969 at the Institut des Hautes Études advisor
Scientifiques. Between 1977 and 1978 he was visiting Doctoral Lawrence Schulman
professor at the École Polytechnique in Paris and in students Huzihiro Araki
1982 at the University of Adelaide.[6]
Richard Ferrell
Wightman has been married twice. His first wife, Stephen Fulling
Anna-Greta Larsson, was an artist and photographer Arthur Jaffe
and died early. They had a daughter, Robin, who also Oscar Lanford
Jerrold Marsden
Eduard Prugovecki
Silvan S. Schweber
Barry Simon
died prematurely. The second wife was the Bulgarian Alan Sokal
translator Ludmilla Popova Wightman. Wightman died
on January 13, 2013, in Princeton, in New Jersey.[7]

Scientific career
Already during his undergraduate studies, Arthur Wightman had close contacts with the mathematics
department in Princeton. Together with the mathematician John Tate, Wightman was engaged in the work
on the Lorentz and Poincaré groups representations.[8]

In the 1950s, he introduced his Wightman axioms as a mathematical foundation to relativistic quantum
field theory. Quantum fields are treated as 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, , could be analytically continued to all separations .[9]: 425 Using this, Res Jost
was able to derive the PCT and the spin-statistics theorems, as shown in Wightman's and Streater's
book.[10] Together with Eugene Wigner and Gian-Carlo Wick, he introduced superselection rules and
studied the representations of commutator and anti-commutator algebras with the mathematician Lars
Gårding.[11]

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[12] and in 1997 the Henri
Poincaré Prize of the International Association of Mathematical Physics[13] for his central role in the
foundations of the general theory of quantum fields.[2] Since 1964 he was a fellow of the American
Physical Society,[14] since 1966 of the American Academy of Arts and Sciences,[15] and since 1970 of the
United States National Academy of Sciences.[16] In 1962 he was an invited speaker at the International
Congress of Mathematicians in Stockholm.[17] In 1976 he was Josiah Willard Gibbs Lecturer.[18]

Selected publications
Streater, Raymond F.; Wightman, Arthur S. (1989). PCT, spin and statistics, and all that.
ISBN 978-0691070629.
Wightman, Arthur S. (1956). "Quantum Field Theory in Terms of Vacuum Expectation
Values". Physical Review. 101 (2): 860–866. Bibcode:1956PhRv..101..860W (https://ui.adsa
bs.harvard.edu/abs/1956PhRv..101..860W). doi:10.1103/PhysRev.101.860 (https://doi.org/1
0.1103%2FPhysRev.101.860).
Wightman, Arthur S.; Gårding, Lars (1965). "Fields as operator-valued distributions in
relativistic quantum theory". Arkiv för Fysik. 28.
Wightman, Arthur S. (1969). "What is the point of so-called axiomatic field theory?". Physics
Today. 22 (9): 53–58. Bibcode:1969PhT....22i..53W (https://ui.adsabs.harvard.edu/abs/1969
PhT....22i..53W). doi:10.1063/1.3035782 (https://doi.org/10.1063%2F1.3035782).
 Wightman, Arthur S. (1967). Introduction to some aspects of the relativistic dynamics of
quantized fields, Cargese Lectures in Theoretical Physics. Gordon and Breach Science
Publishers.
Wightman, Arthur S. (1977). "Should We Believe in Quantum Field Theory?". 15th Erice
School of Subnuclear Physics: The Why's of Subnuclear Physics. pp. 983–1025.
Wick, Gian Carlo; Wightman, Arthur S.; Wigner, Eugene P. (1952). "The intrinsic parity of
elementary particles". Physical Review. 88 (1): 101–105. Bibcode:1952PhRv...88..101W (htt
ps://ui.adsabs.harvard.edu/abs/1952PhRv...88..101W). doi:10.1103/PhysRev.88.101 (http
s://doi.org/10.1103%2FPhysRev.88.101).
Wightman, Arthur S. (1981). "Looking back at quantum field theory". Physica Scripta. 24 (5):
813–816. doi:10.1088/0031-8949/24/5/001 (https://doi.org/10.1088%2F0031-8949%2F24%
2F5%2F001).
Jaffe, Arthur; Wightman, Arthur S.; Jost, Res (1990). "For Res Jost, and To Arthur
Wightman" (https://projecteuclid.org/euclid.cmp/1104201026). Communications in
Mathematical Physics. 132 (1): 1–4. doi:10.1007/BF02277996 (https://doi.org/10.1007%2FB
F02277996).
Wightman, Arthur S. (1989). "The theory of quantized fields in the 50s". Pions to Quarks:
Particle Physics in the 50s. 50: 255–261.

See also

Physics portal

Biography portal

Axiomatic quantum field theory

Hilbert's sixth problem
PCT Theorem
Principle of locality
Quantum field theory
Wightman axioms
Wightman functional

References
1. Kelly, Morgan (January 30, 2013). "Princeton University - Esteemed Princeton mathematical
physicist and mentor Arthur Wightman dies" (http://www.princeton.edu/main/news/archive/S
35/94/19A97/index.xml?section=topstories). Princeton.edu. Retrieved February 13, 2013.
2. "Wightman's Henri Poincaré Prize citation" (http://www.iamp.org/poincare/aw97-cit.html).
International Association of Mathematical Physics. Retrieved March 9, 2021.
3. The doctoral thesis is Wightman, Arthur (1949). The Moderation and Absorption of Negative
Pions in Hydrogen (https://ui.adsabs.harvard.edu/abs/1949PhDT........16W/abstract)
(Thesis). Princeton. Bibcode:1949PhDT........16W (https://ui.adsabs.harvard.edu/abs/1949P
hDT........16W).
4. Simon, Barry, ed. (March 2015). "In Memory of Arthur Strong Wightman" (https://www.ams.o
rg/notices/201503/rnoti-p249.pdf) (PDF). Notices of the AMS. 62 (3): 249–257.
doi:10.1090/noti1219 (https://doi.org/10.1090%2Fnoti1219).
 5. Aizenman, Michael; Lieb, Elliott; Nelson, Edward. "Arthur Strong Wightman 1922-2013" (htt
ps://phy.princeton.edu/department/history/faculty-history/arthur-wightman). Princeton
University. Retrieved March 9, 2021.
6. "Biography from the APS" (https://web.archive.org/web/20151222231720/https://www.aip.or
g/history/acap/biographies/bio.jsp?wightmana). aip.org. Archived from the original (https://w
ww.aip.org/history/acap/biographies/bio.jsp?wightmana) on December 22, 2015.
7. Jaffe, Arthur; Simon, Barry (January 2013). "Arthur Strong Wightman (1922–2013)" (http://m
ath.caltech.edu/SimonPapers/R57.pdf) (PDF). News Bulletin, International Association of
Mathematical Physics: 34–36.
8. Jaffe, Arthur; Wightman, Arthur S.; Jost, Res (1990). "For Res Jost, and To Arthur
Wightman" (https://projecteuclid.org/euclid.cmp/1104201026). Communications in
Mathematical Physics. 132 (1): 1–4. doi:10.1007/BF02277996 (https://doi.org/10.1007%2FB
F02277996).
9. Duck, Ian; Sudarshan, Ennackel Chandy George; Sudarshan, E. C. G. (1998). Pauli and the
spin-statistics theorem (1. reprint ed.). Singapore: World Scientific. ISBN 978-981-02-3114-
9.
10. Streater, Raymond F.; Wightman, Arthur S. (1989). PCT, spin and statistics, and all that.
ISBN 978-0691070629.
11. Streater, Ray. "Table of contents, Streater, Wightman PCT, Spin, Statistics and all that" (http
s://web.archive.org/web/20120716210613/http://www.mth.kcl.ac.uk/~streater/PCT.html).
mth.kcl.ac.uk. Archived from the original (http://www.mth.kcl.ac.uk/~streater/PCT.html) on
July 16, 2012.
12. "1969 Dannie Heineman Prize for Mathematical Physics Recipient" (https://www.aps.org/pro
grams/honors/prizes/prizerecipient.cfm?first_nm=Arthur&last_nm=Wightman&year=1969).
American Physical Society. Retrieved March 9, 2021.
13. "Henri Poincaré Prize winners" (http://www.iamp.org/page.php?page=page_prize_poincare).
International Association of Mathematical Physics. Retrieved March 9, 2021.
14. "APS Fellow Archive" (https://www.aps.org/programs/honors/fellowships/archive-all.cfm?initi
al=W&year=1964). American Physical Society. Retrieved March 9, 2021.
15. "American Academy of Arts and Sciences member page of Arthur Wightman" (https://www.a
macad.org/person/arthur-strong-wightman). National Academy of Sciences. Retrieved
March 9, 2021.
16. "National Academy of Sciences member page of Arthur Wightman" (http://www.nasonline.or
g/member-directory/deceased-members/49130.html). National Academy of Sciences.
Retrieved March 6, 2021.
17. "International Congress of Mathematicians. List of Members, Stockholm 1962" (https://www.
mathunion.org/fileadmin/ICM/Proceedings/ICM1962.4/ICM1962.4.ocr.pdf) (PDF).
International Mathematical Union. Retrieved March 9, 2021.
18. "Josiah Willard Gibbs Lectures" (https://www.ams.org/meetings/lectures/meet-gibbs-lect).
American Mathematical Society. Retrieved March 9, 2021.

Further reading
Simon, Barry, ed. (March 2015). "In Memory of Arthur Strong Wightman" (https://www.ams.o
rg/notices/201503/rnoti-p249.pdf) (PDF). Notices of the AMS. 62 (3): 249–257.
doi:10.1090/noti1219 (https://doi.org/10.1090%2Fnoti1219).
Kelly, Morgan (January 30, 2013). "Esteemed Princeton mathematical physicist and mentor
Arthur Wightman dies" (http://www.princeton.edu/main/news/archive/S35/94/19A97/index.x
ml?section=topstories). Princeton University. Retrieved March 10, 2021.
 Aizenman, Michael; Lieb, Elliott; Nelson, Edward. "Arthur Strong Wightman 1922-2013" (htt
ps://phy.princeton.edu/department/history/faculty-history/arthur-wightman). Princeton
University. Retrieved March 9, 2021.
Jaffe, Arthur; Simon, Barry (January 2013). "Arthur Strong Wightman (1922–2013)" (http://m
ath.caltech.edu/SimonPapers/R57.pdf) (PDF). News Bulletin, International Association of
Mathematical Physics: 34–36.

External links
Arthur Wightman (https://mathgenealogy.org/id.php?id=11904) at the Mathematics
Genealogy Project.
Literature by and about Arthur Wightman (https://portal.dnb.de/opac.htm?method=simpleSe
arch&cqlMode=true&query=idn%3D1057560499) in the German National Library catalogue.
Arthur Wightman (https://zbmath.org/authors/?q=ai:wightman.arthur-s) at zbMATH.
Streater, Ray. "Remarks with photo" (https://web.archive.org/web/20030819031511/http://w
ww.mth.kcl.ac.uk/~streater/wightman.html). mth.kcl.ac.uk. Archived from the original (http://
www.mth.kcl.ac.uk/~streater/wightman.html) on August 19, 2003.
Streater, Ray. "Table of contents, Streater, Wightman PCT, Spin, Statistics and all that" (http
s://web.archive.org/web/20120716210613/http://www.mth.kcl.ac.uk/~streater/PCT.html).
mth.kcl.ac.uk. Archived from the original (http://www.mth.kcl.ac.uk/~streater/PCT.html) on
July 16, 2012.
"Biography from the APS" (https://web.archive.org/web/20151222231720/https://www.aip.or
g/history/acap/biographies/bio.jsp?wightmana). aip.org. Archived from the original (https://w
ww.aip.org/history/acap/biographies/bio.jsp?wightmana) on December 22, 2015.
"Wightman's Henri Poincaré Prize citation" (http://www.iamp.org/poincare/aw97-cit.html).
International Association of Mathematical Physics. Retrieved March 9, 2021.

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