Huzihiro Araki

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 at the Kyoto University Gentaro Araki, with whom he studied and with which he published in 1954 his first work. He made his diploma with Hideki Yukawa and he 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 a professor at Kyoto University, the Research Institute for Mathematical Sciences ( RIMS), whose director he was.

Araki dealt with axiomatic quantum field theory and statistical mechanics, in particular by the use of operator algebras ( von Neumann algebras, C *-algebras ). He made ​​back in the early 1960s in Princeton important contributions to the Local Quantum Physics of Haag and Kastler and also to the scattering theory of Haag and David Ruelle. He also did important contributions to the mathematical theory of operator algebras, so the classification of type III factors of von Neumann algebras. He originated the concept of relative entropy of states of von Neumann algebras. In the 1970s, he showed the equivalence of the KMS ( Kubo -Martin -Schwinger ) condition for the characterization of quantum mechanical states in thermodynamic equilibrium to variational principles in quantum spin systems on lattices. With Yanase he also dealt with the basics of quantum mechanics ( Wigner- Araki - Yanase theorem, the limitations of the measurement process by conservation laws describing ).

He was in 1979 the second president of the International Association of Mathematical Physics. In 2003 he received with Oded Schramm and Elliott Lieb the Henri Poincaré Prize. 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 1978 in Helsinki ( Some topics in quantum statistical mechanics ). He is a Fellow of the American Mathematical Society.

Writings (selection )

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