Paul Robert Chernoff (21 June 1942,

Philadelphia Philadelphia, often called Philly, is the largest city in the Commonwealth of Pennsylvania, the sixth-largest city in the U.S., the second-largest city in both the Northeast megalopolis and Mid-Atlantic regions after New York City. Sinc ...

– 17 January 2017) was an American mathematician, specializing in functional analysis and the mathematical foundations of quantum mechanics. He is known for Chernoff's Theorem, a mathematical result in the Feynman path integral formulation of quantum mechanics.

Education and career

Chernoff graduated from Central High School in Philadelphia. He matriculated at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, where he received bachelor's degree ''summa cum laude'' in 1963, master's degree in 1965, and Ph.D. in 1968 under

George Mackey George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician known for his contributions to quantum logic, representation theory, and noncommutative geometry. Career Mackey earned his bachelor of arts at Rice Unive ...

with thesis ''Semigroup Product Formulas and Addition of Unbounded Operators''. At the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

he became in 1969 a lecturer, in 1971 an assistant professor, and in 1980 a full professor. U. C. Berkeley awarded him multiple Distinguished Teaching Awards and the Lili Fabilli and Eric Hoffer Essay Prize. In 1986 he was a visiting professor at the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

. Chernoff was elected in 1984 a Fellow of the

American Association for the Advancement of Science The American Association for the Advancement of Science (AAAS) is an American international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific respons ...

and in 2012 a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. He gave in 1981 a simplified proof of the Groenewold- Van Hove theorem, which is a

no-go theorem In theoretical physics, a no-go theorem is a theorem that states that a particular situation is not physically possible. Specifically, the term describes results in quantum mechanics like Bell's theorem and the Kochen–Specker theorem that cons ...

that relates classical mechanics to quantum mechanics.

Selected publications

*Note on product formulas for operator semigroups, J. Funct. Analysis, vol. 2, 1968, pp. 238–242 *with Richard Anthony Rasala and William C. Waterhouse
The Stone-Weierstrass theorem for valuable fields
Pacific Journal of Mathematics vol. 27, no. 2, 1968, pp. 233–240 *Some remarks on quasi-analytic vectors, Trans. Amer. Math. Soc. vol. 167, 1972, pp. 105–113 *Representations, automorphisms, and derivations of some operator algebras, J. Funct. Analysis, vol. 12, 1973, pp. 275–289 *Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Analysis, vol. 12, 1973, pp. 401–414
Product formulas, nonlinear semigroups, and addition of unbounded operators
American Mathematical Society 1974. *with

Jerrold Marsden Jerrold Eldon Marsden (August 17, 1942 – September 21, 2010) was a Canadian mathematician. He was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology.. Marsden is listed as an IS ...

Properties of infinite dimensional Hamiltonian systems
Springer 1974
Understanding mathematical proofs: Conceptual barriers
Science vol. 193, no. 4250, 1976, p. 276
The quantum ''n''-body problem and a theorem of Littlewood
Pacific J. Math., vol. 70, 1977, pp. 117–123 *Irreducible representations of infinite-dimensional transformation groups and Lie algebras, I. J. Funct. Anal., vol. 130, 1995, pp. 255–282 *with

Rhonda Hughes Rhonda Jo Hughes (born Rhonda Weisberg September 28, 1947). is an American mathematician, the Helen Herrmann Professor Emeritus of Mathematics at Bryn Mawr College.

: "A new class of point interactions in one dimension." Journal of functional analysis, vol. 111, no. 1, 1993, pp. 97–117 *with R. Hughes: Some examples related to Kato's conjecture. J. Austral. Math. Soc. Ser. A, vol. 60, 1996, pp. 274–286.
Quantization and irreducible representations of infinite-dimensional transformation groups and Lie algebras
In: Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory (Berkeley, CA, 1999), Eletron. J. Differ. Equ. Conf., vol. 4, 2000, pp. 17–22 *A pseudo zeta function and the distribution of primes, Proc. Natl. Acad. Sci. USA, vol. 97, 2000, pp. 7697–7699 (There is a typographical error: "One can show that C(s) may be analytically continued at least into the half-plane Re s > 0 except for an isolated singularity (presumably a simple pole) at s = 0." This should be "at s = 1" according to the mathematical argument given.)

References

{{DEFAULTSORT:Chernoff, Paul 1942 births 2017 deaths 20th-century American mathematicians 21st-century American mathematicians Mathematical analysts Central High School (Philadelphia) alumni Harvard College alumni University of California, Berkeley College of Letters and Science faculty Fellows of the American Association for the Advancement of Science Fellows of the American Mathematical Society Harvard Graduate School of Arts and Sciences alumni