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 algebras, 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, Yanase 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 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. In 2012 he became a fellow of the American Mathematical Society.
- Mathematical theory of quantum fields, Oxford University Press 1999
- Araki, E.J. Woods A classification of factors, Pub. RIMS, Ser.A, Bd.4, 1968, S.51-130. Araki A classification of factors II, Pub. RIMS, Bd.4, 1968, S.585
- Araki On the equivalence of the KMS condition and the variational principle for quantum lattice systems, Comm. Math.Phys., Bd. 38, 1974, S.1, Araki, Sewell KMS conditions and local thermodynamic stability of quantum lattice systems, Comm.Math.Phys. Bd.52, 1977, S.103-109
- Araki, Yanase Measurement of quantum mechanical operators, Physical Review Vol.120, 1960, p.622, Wigner Zeitschrift für Physik Bd.131, 1952, S.101.
- Yanase, M.M. Optimal Measurement Apparatus, Physical Review Vol.123, 1961, p. 666
- "The Henri Poincaré Prize". International Association of Mathematical Physics. Retrieved 2010-07-11.
- List of Fellows of the American Mathematical Society, retrieved 2012-11-03.
- Laudatio by Longo for Araki's Poincare Prize, pdf
- Alain Connes, Moshe Flato, Heisuke Hironaka, Arthur Jaffe, Vaughan Jones, appreciation in Comm.Math.Phys. Vol.155, 1993, p.1
- Huzihiro Araki at the Mathematics Genealogy Project