Huzihiro Araki
Encyclopedia
is a Japanese mathematical physicist and mathematician.
Araki is the son of the University of Kyoto physics professor Gentarō Araki, with whom he studied and with whom in 1954 he published his first physics paper. He earned his diploma under Hideki Yukawa
and in 1960 he attained his doctorate at Princeton University
with thesis advisors 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), of which he was also the director.
Araki works on axiomatic quantum field theory
and statistical mechanics
in particular on application of operator algebras (von Neumann algebra
s, C*-algebras). He already at the beginning of the 1960s at Princeton made important contributions to the "local quantum physics" of Haag and Kastler and also to the scattering theories of Haag and David Ruelle
. He also supplied important contributions in the mathematical theory of operator algebras, classifying type-III factors of von Neumann algebras. Araki originated the concept of relative entropy of states of Von Neumann algebras. In the 1970s he showed the equivalence in quantum thermodynamics of, on the one hand, the KMS (Kubo-Martin-Schwinger) condition
for the characterization of quantum mechanical states in thermodynamic equilibrium with, on the other hand, the variational principle for quantum mechanical spin systems on lattices. With Yanase he worked on the foundations of quantum mechanics (Wigner-Araki-Yanase Theorem, which describes restrictions that conservation laws impose upon the physical measuring process). Stated in more precise terms, they proved that an exact measurement of an operator, which additively replaces the operator with a conserved size, is impossible. However, Araki did prove that the uncertainty of the measurement can be made arbitrarily small, provided that the measuring apparatus is sufficiently large.
He was the first president of the International Association of Mathematical Physics
. In he 2003 he received with Oded Schramm
and Elliott Lieb the Henri Poincaré Prize. In 1990 he was the chief organizer of the ICM
in Kyoto. He is one of the editors of the Communications in Mathematical Physics and founder of Reviews in Mathematical Physics.
Araki is the son of the University of Kyoto physics professor Gentarō Araki, with whom he studied and with whom in 1954 he published his first physics paper. He earned his diploma under Hideki Yukawa
Hideki Yukawa
né , was a Japanese theoretical physicist and the first Japanese Nobel laureate.-Biography:Yukawa was born in Tokyo and grew up in Kyoto. In 1929, after receiving his degree from Kyoto Imperial University, he stayed on as a lecturer for four years. After graduation, he was interested in...
and in 1960 he attained his doctorate at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
with thesis advisors Rudolf Haag
Rudolf Haag
Rudolf Haag is a German physicist. He is best known for his contributions to the algebraic formulation of axiomatic quantum field theory, namely the Haag-Kastler axioms...
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), of which he was also the director.
Araki works on axiomatic quantum field theory
Axiomatic quantum field theory
Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years from a more geometric and functorial...
and statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
in particular on application of operator algebras (von Neumann algebra
Von Neumann algebra
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann, motivated by his study of single operators, group...
s, C*-algebras). He already at the beginning of the 1960s at Princeton made important contributions to the "local quantum physics" of Haag and Kastler and also to the scattering theories of Haag and David Ruelle
David Ruelle
David Pierre Ruelle is a Belgian-French mathematical physicist. He has worked on statistical physics and dynamical systems. With Floris Takens he coined the term strange attractor, and founded a new theory of turbulence...
. He also supplied important contributions in the mathematical theory of operator algebras, classifying type-III factors of von Neumann algebras. Araki originated the concept of relative entropy of states of Von Neumann algebras. In the 1970s he showed the equivalence in quantum thermodynamics of, on the one hand, the KMS (Kubo-Martin-Schwinger) condition
KMS state
In the statistical mechanics of quantum mechanical systems and quantum field theory, the properties of a system in thermal equilibrium can be described by a mathematical object called a Kubo-Martin-Schwinger state or, more commonly, a KMS state.-Preliminaries:...
for the characterization of quantum mechanical states in thermodynamic equilibrium with, on the other hand, the variational principle for quantum mechanical spin systems on lattices. With Yanase he worked on the foundations of quantum mechanics (Wigner-Araki-Yanase Theorem, which describes restrictions that conservation laws impose upon the physical measuring process). Stated in more precise terms, they proved that an exact measurement of an operator, which additively replaces the operator with a conserved size, is impossible. However, Araki did prove that the uncertainty of the measurement can be made arbitrarily small, provided that the measuring apparatus is sufficiently large.
He was the first president of the International Association of Mathematical Physics
International Association of Mathematical Physics
The International Association of Mathematical Physics was founded in 1976 to promote research in mathematical physics. It brings together research mathematicians and theoretical physicists, including students. The association's ordinary members are individual researchers, although associate...
. In he 2003 he received with Oded Schramm
Oded Schramm
Oded Schramm was an Israeli-American mathematician known for the invention of the Schramm–Loewner evolution and for working at the intersection of conformal field theory and probability theory.-Biography:...
and Elliott Lieb the Henri Poincaré Prize. In 1990 he was the chief organizer of the ICM
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in Kyoto. He is one of the editors of the Communications in Mathematical Physics and founder of Reviews in Mathematical Physics.