Huzihiro Araki

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Huzihiro Araki ( Japanese 荒木 不二 洋 , Araki Fujihiro ; born July 28, 1932 ) is a Japanese mathematical physicist and mathematician.

Araki is the son of the physics professor of the University of Kyoto Gentarō Araki, with whom he studied and with whom he published his first work in 1954. He completed his diploma with Hideki Yukawa and received his doctorate in 1960 from Princeton University with Rudolf Haag and Arthur Strong Wightman ( Hamiltonian formalism and canonical commutation relations in quantum field theory ). He was since 1966 professor at the University of Kyoto, at the Research Institute for Mathematical Sciences (RIMS), whose director he was also.

Araki dealt with axiomatic quantum field theory and statistical mechanics , in particular using operator algebras ( Von Neumann algebras , C * algebras ). In the early 1960s in Princeton, he made important contributions to the local quantum physics of Haag and Kastler and also to the scattering theory of Haag and David Ruelle . He also made important contributions to the mathematical theory of operator algebras, such as the classification of type III factors of Von Neumann algebras. The concept of the relative entropy of states of Von Neumann algebras comes from him . In the 1970s he showed the equivalence of the KMS (Kubo-Martin-Schwinger) condition for characterizing quantum mechanical states in thermodynamic equilibrium to the principles of variation in quantum mechanical spin systems on grids. With Yanase he also dealt with the fundamentals of quantum mechanics (Wigner-Araki-Yanase theorem, which describes the limitations of the measurement process by conservation laws).

He was second president of the International Association of Mathematical Physics in 1979 . In 2003 he received the Henri Poincaré Prize with Oded Schramm and Elliott Lieb . In 1990 he was the main organizer of the ICM in Kyoto. He is one of the editors of Communications in Mathematical Physics and founder of Reviews in Mathematical Physics . In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( Some topics in the theory of operator algebras ) and in Helsinki in 1978 ( Some topics in quantum statistical mechanics ). He is a fellow of the American Mathematical Society .

Fonts (selection)

  • Mathematical theory of quantum fields . 1999. New edition. Oxford University Press, Oxford 2009, ISBN 978-0-19-956640-2 .

Web links

Individual evidence

  1. ↑ Araki, EJ Woods A classification of factors , Pub. RIMS, Ser. A, Vol. 4, 1968, pp. 51-130. Araki A classification of factors II , Pub. RIMS, Vol. 4, 1968, p. 585
  2. ^ Araki On the equivalence of the KMS condition and the variational principle for quantum lattice systems , Comm. Math. Phys., Vol. 38, 1974, p. 1, Araki, Sewell KMS conditions and local thermodynamic stability of quantum lattice systems , Comm. Math. Phys . Vol. 52, 1977, pp. 103-109
  3. ↑ Araki, Yanase Measurement of quantum mechanical operators , Physical Review Vol. 120, 1960, p. 622, Wigner Zeitschrift für Physik Vol. 131, 1952, p. 101. More precisely, they proved that an exact measurement of an operator working with a (additive) conservation quantity swapped, is impossible. Araki proved, however, that the measurement uncertainty can be made arbitrarily small if the measuring apparatus is sufficiently large, Araki Optimal Measurement Apparatus , Physical Review Vol. 123, 1961, p. 666
personal data
SURNAME Araki, Huzihiro
ALTERNATIVE NAMES 荒木 不二 洋 (Japanese); Araki Fujihiro (Hepburn Romanization)
BRIEF DESCRIPTION Japanese physicist
DATE OF BIRTH July 28, 1932