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Irving Segal

Irving Ezra Segal (1918–1998) was an American mathematician known for work on theoretical quantum mechanics. He shares credit for what is often referred to as the Segal–Shale–Weil representation.[1][2][3] Early in his career Segal became known for his developments in quantum field theory and in functional and harmonic analysis, in particular his innovation of the algebraic axioms known as C*-algebra.

Biography[edit]

Irving Ezra Segal was born in the Bronx on September 13, 1918, to Jewish parents.[4] He attended school in Trenton. In 1934 he was admitted to Princeton University, at the age of 16. He was elected to Phi Beta Kappa, completed his undergraduate studies in just three years time, graduated with highest honors with a bachelor's degree in 1937, and was awarded the George B. Covington Prize in Mathematics. He was then admitted to Yale, and in another three years time had completed his doctorate, receiving his Doctor of Philosophy degree in 1940. Segal taught at Harvard University, then he joined the Institute for Advanced Study in Princeton on a Guggenheim Memorial Fellowship, working from 1941 to 1943 with Albert Einstein and John von Neumann. During World War II Segal served in the US Army conducting research in ballistics at the Aberdeen Proving Ground in Maryland. He joined the mathematics department at the University of Chicago in 1948 where he served until 1960. In 1960 he joined the mathematics department at the Massachusetts Institute of Technology where he remained as a professor until his death in 1998. During his career he supervised 40 doctoral students — 15 at the University of Chicago and 25 at M.I.T.[5] He won three Guggenheim Fellowships, in 1947, 1951 and 1967, and received the Humboldt Award in 1981. He was an Invited Speaker of the International Congress of Mathematicians in 1966 in Moscow and in 1970 in Nice. He was elected to the National Academy of Sciences in 1973.


In 1983 Victor Guillemin edited a festschrift dedicated to Irving Segal.[6] Physics Today published a review of Introduction to Algebraic and Constructive Quantum Field Theory (1992), which Segal coauthored.[7]


Segal died in Lexington, Massachusetts, on August 30, 1998. Edward Nelson's obituary article about Segal concludes: "... It is rare for a mathematician to produce a life work that at the time can be fully and confidently evaluated by no one, but the full impact of the work of Irving Ezra Segal will become known only to future generations."[8]

1951: Segal, Irving Ezra (1951). . Memoirs of the American Mathematical Society, no. 9. ISBN 9780821812099.

Decompositions of operator algebras, I and II

1962: Lectures at the Boulder Summer Seminar,

American Mathematical Society

1963: . Lectures in Applied Mathematics, vol. 2. American Mathematical Soc. 1967; with an appendix by George W. Mackey{{cite book}}: CS1 maint: postscript (link)

Mathematical problems of relativistic physics

1968: (with ) Integrals and operators. McGraw-Hill. 1968. Revised & enlarged 2nd edition. Grundlehren der mathematische Wissenschaften, vol. 228. Springer-Verlag. 2012-12-06. ISBN 9783642666933; pbk reprint of 1978 2nd edition{{cite book}}: CS1 maint: postscript (link)

Ray Kunze

1976: . Pure and Applied Mathematics Series, Vol. 68. Academic Press. 1976-02-19. ISBN 9780080873848.

Mathematical cosmology and extragalactic astronomy

1992: (with and Zhengfang Zhou) Baez, J. C.; Segal, I. E.; Zhou, Z.; Kon, Mark A. (1993). "Introduction to algebraic and constructive quantum field theory". Physics Today. 46 (12). Princeton University Press: 43. Bibcode:1993PhT....46l..43B. doi:10.1063/1.2809125. Baez, John C.; Segal, Irving E.; Zhou, Zhengfang (2014-07-14). 2014 reprint. Princeton University Press. ISBN 9781400862504.

John C. Baez

1993: (with Nicoll, J.F., Wu, P., Zhou, Z.) , The Astrophysical Journal 465–484

Statistically Efficient Testing of the Hubble and Lundmark Laws on IRAS Galaxy Samples

1995: (with Zhou, Z.) , ApJS. Ser. 100, 307–324

Maxwell's Equations in the Einstein Universe and Chronometric Cosmology

1997: "Cosmic time dilation", The Astrophysical Journal 482:L115–17

For a list of 227 articles and 10 books to which Segal contributed, see the MIT external link below.

Commutation theorem for traces

Metaplectic group

Symplectic group

Symplectic spinor bundle

Habermann, Katharina; Habermann, Lutz (2006), Introduction to Symplectic Dirac Operators, , ISBN 978-3-540-33420-0

Springer-Verlag

at the Mathematics Genealogy Project

Irving Segal

(PDF). math.mit.edu.

"Publications of Irving Segal"

(1999) Memories of Irving Segal

John C. Baez

Leonard Gross and William Segal, "Irving E. Segal", Biographical Memoirs of the National Academy of Sciences (2022)