Paul Chernoff

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Paul Chernoff

Paul Robert Chernoff (born June 21, 1942 in Philadelphia , † January 17, 2017 ) was an American mathematician .

Career

Chernoff attended Central High School in Philadelphia and studied at Harvard University with a bachelor's degree summa cum laude in 1963, a master's degree in 1965, and a doctorate from George Mackey in 1968 (Semigroup Product Formulas and Addition of Unbounded Operators). He became a lecturer at Berkeley in 1969 , assistant professor in 1971 and professor in 1980.

In 1986 he was visiting professor at the University of Pennsylvania .

He dealt with functional analysis (operator theory) and especially mathematical aspects of the fundamentals of quantum mechanics.

He was a fellow of the American Association for the Advancement of Science and the American Mathematical Society .

A theorem, which he proved in 1968, about product formulas of semigroups of operators supports Feynman's path integral formulation of quantum mechanics from a mathematical point of view.

He also gave a simple proof of the Groenewold and van Hove Theorem in 1981. This concerns the correspondence between classical and quantum mechanics found by Paul Dirac , in which Poisson brackets are replaced by commutators of operators (which is carried out for polynomials in variables with degrees less than or equal to 2). The theorem of Groenewold and van Hove says that this cannot be extended to a Poisson sub-algebra of the algebra of polynomials that contains all polynomials of degree less than or equal to 2 (i.e. there is no extension of Dirac's quantization method to polynomials higher than second degree ).

Fonts

  • Note on product formulas for operator semigroups, J. Funct. Analysis, Vol. 2, 1968, pp. 238-242
  • Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Analysis, Vol. 12, 1973, p. 401
  • with Jerrold Marsden : Properties of infinite dimensional Hamiltonian systems, Springer 1974
  • The quantum n-body problem and a theorem of Littlewood, Pacific J. Math., Vol. 70, 1977, pp. 117-123
  • 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.
  • with Rhonda Hughes: Some examples related to Kato's conjecture. J. Austral. Math. Soc. Ser. A, Vol. 60, 1996, pp. 274-286.
  • Irreducible representations of infinite-dimensional transformation groups and Lie algebras. IJ Funct. Anal., Vol. 130, 1995, pp. 255-282

Web links

Individual evidence

  1. ↑ Birth and career data according to American Men and Women of Science , Thomson Gale 2004
  2. ↑ Paul Chernoff in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  3. ↑ Chernoff, Mathematical obstructions to quantization, Hadronic J., Volume 4, 1981, pp. 879-898
  4. ↑ Represented in Shlomo Sternberg, Victor Guillemin, Symplectic Techniques in Physics, Cambridge UP, 1990, p. 101
  5. ^ Rolf Berndt, Introduction to Symplectic Geometry, Vieweg, 1998, p. 119
personal data
SURNAME Chernoff, Paul
ALTERNATIVE NAMES Chernoff, Paul Robert (full name)
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH June 21, 1942
PLACE OF BIRTH Philadelphia
DATE OF DEATH 17th January 2017