Irving Segal
Irving Ezra Segal (* September 13, 1918 in the Bronx, New York City; † 24 December 1998 in Lexington, Massachusetts) was an American mathematician who worked on functional analysis, harmonic analysis, C *-algebras and mathematical quantum field theory.
Life
Segal attended school in Trenton (New Jersey) and started from 1934 to study at Princeton University, where he in 1937 with top marks earned his bachelor 's degree. In 1940 he received his doctorate at Einar Hille at Yale University with the thesis ring Properties of Certain Classes of Functions. In 1941 he was instructor at Harvard University, 1941-1943 Research Associate at Princeton and from 1945 to 1948 at the Institute for Advanced Study in Princeton, where he worked with Albert Einstein and John von Neumann. In between, he worked in World War II during his military service at the Aberdeen Proving Ground U.S. Army in ballistics. In 1948 he became an assistant professor at the University of Chicago, 1953 Associate Professor and Professor in 1957. 1960 he transferred to the Massachusetts Institute of Technology (MIT ), where he was a professor until his death ( in 1989 as Emeritus). He was a visiting professor at, among others, the Sorbonne, the Collège de France, in Moscow, Copenhagen, Lund, Pisa and Columbia University.
Segal was in 1947, 1951 and 1967 Guggenheim Fellow. In 1981 he received the Humboldt Prize. In 1973 he was elected to the National Academy of Sciences. He was also a member of the American Academy of Arts and Sciences and the Royal Danish Academy of Sciences.
In the functional analysis, generalizing the work of Norbert Wiener on stochastic processes in Hilbert spaces, developed a theory of noncommutative integration and generalized so that the set of Plancherel for locally compact groups. His name is connected to the GNS - construction in which the S stands for Segal.
Segal was very interested in mathematical physics (he was not only a member of the AMS, but also the American Astronomical and Physical Society ). He was the first to recognize the importance of C * - algebras as observables algebras for the formulation of axiomatic quantum field theory. In 1947 he used them for a mathematical reformulation of the postulates of quantum mechanics. In the early 1960s he organized two conferences to at MIT - but the further development of the area in the 1960s by James Glimm and Arthur Jaffe was not to his taste.
Segal declined to unconventional perspectives. He was further of an alternative ( " chronometric " ) theory to explain the redshift galaxies as a geometric effect (rather than as evidence of expansion of the universe after the Big Bang ), which he sought to substantiate the statistical analysis of astronomical spectra. The origin of his speculations was in his studies of 1951 on the deformation of Lie algebras. Just as the Galilei group is a limiting case of the Lorentz group of special relativity (and this deformation of the Galilei group), the Lorentz group is a limiting case of the more general conformal group, which is the actual symmetry group of the universe according to Segal.
In 1966 he was invited speaker on the ICM in Moscow ( Nonlinear relativistic partial differential equations ) and in 1970 in Nice ( Nonlinear quantum processes and automorphism groups of C * algebras ).
His students include John Baez, Isadore Singer, Edward Nelson and Bertram Kostant. He was married twice and had three children from his first marriage and a daughter from his second marriage.
Writings
- Segal, Baez, Zhou: Introduction to Algebraic and Constructive Quantum Field Theory. Princeton 1992.
- Mathematical cosmology and extragalactic astronomy. Academic Press 1976.
- Integral and operator. McGraw Hill 1968, Springer-Verlag 1978.
- Mathematical Problems in Relativistic Physics. AMS 1963 ( with appendix of George Mackey ).