Huzihiro Araki

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 Wightman.The thesis is {{cite thesis|last=Araki|first=Huzihiro|date=1960|title=Hamiltonian formalism and the canonical commutation relations in quantum field theory|journal=Journal of Mathematical Physics|volume=1|number=6|pages=492–504}} He was a professor at the University of Kyoto starting in 1966, and became the director of the Research Institute for Mathematical Sciences (RIMS).

Araki died on 16 December 2022.

Araki worked on axiomatic quantum field theory, statistical mechanics, and in particular on applications of operator algebras like von Neumann algebras and C*-algebras. At the beginning of the 1960s, in Princeton, he made important contributions to local quantum physics and to the scattering theories of Haag and David Ruelle. He also supplied important contributions in the mathematical theory of operator algebras, classifying the type-III factors of von Neumann algebras.{{Cite journal|last1=Araki|first1=Huzihiro|last2=Woods|first2=E. J.|title=A classification of factors|journal=Publications of the Research Institute for Mathematical Sciences, Kyoto University. Ser. A|volume=4|number=1|pages=51–130|year=1968|doi=10.2977/prims/1195195263|doi-access=free}} 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 condition (named after Ryogo Kubo, Paul C. Martin, and Julian Schwinger) 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.{{Cite journal|last=Araki|first=Huzihiro|title=On the equivalence of the KMS condition and the variational principle for quantum lattice systems|journal=Communications in Mathematical Physics|volume=38|pages=1–10|year=1974|issue=1|doi=10.1007/BF01651545|bibcode=1974CMaPh..38....1A|s2cid=73547157|url=https://projecteuclid.org/euclid.cmp/1103859514}} {{Cite journal|last1=Araki|first1=Huzihiro|last2=Sewell|first2=Geoffrey L.|title=KMS Conditions and Local Thermodynamical Stability of Quantum Lattice Systems|journal=Communications in Mathematical Physics|volume=52|pages=103–109|year=1977|issue=2|doi=10.1007/BF01625778|bibcode=1977CMaPh..52..103A|s2cid=120544596|url=https://projecteuclid.org/euclid.cmp/1103900491}} With Yanase he worked on the foundations of quantum mechanics, i.e. the Wigner-Araki-Yanase theorem, which describes restrictions that conservation laws impose upon the physical measuring process.{{Cite journal|last1=Araki|first1=Huzihiro|last2=Yanase|first2=Mutsuo M.|title=Measurement of Quantum Mechanical Operators|journal=Physical Review|volume=120|pages=622–626|year=1960|issue=2|doi=10.1103/PhysRev.120.622|bibcode=1960PhRv..120..622A}} 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.{{Cite journal|last=Yanase|first=Mutsuo M.|title=Optimal measuring apparatus|journal=Physical Review|volume=123|page=666|year=1961|issue=2|doi=10.1103/PhysRev.123.666|bibcode=1961PhRv..123..666Y}}

Huzihiro Araki was an invited speaker at the International Congress of Mathematicians in 1970 in Nice and in 1978 in Helsinki.{{cite web|title=ICM Plenary and Invited Speakers|website=mathunion.org|url=https://www.mathunion.org/icm-plenary-and-invited-speakers?combine=araki|access-date=20 February 2021}} He was the second president of the International Association of Mathematical Physics, during the period 1979–1981.{{cite web|url=http://www.iamp.org/page.php?page=page_about|title=About the IAMP - Past presidents|website=International Association of Mathematical Physics|access-date=20 February 2021}} In 2003 he received, together with Oded Schramm and Elliott Lieb, the Henri Poincaré Prize.{{cite web|url=http://www.iamp.org/page.php?page=page_prize_poincare|title=The Henri Poincaré Prize|publisher=International Association of Mathematical Physics|access-date=20 February 2021}} In 1990 he was the chief organizer of the International Congress of Mathematicians in Kyoto. He was editor of the scientific journal Communications in Mathematical Physics{{Cite book|last=Zambrini|first=Jean-claude|date=2006|chapter=Laudatio for Huzihiro Araki|title=XIVth International Congress on Mathematical Physics|publisher=World Scientific}} and founder of Reviews in Mathematical Physics.{{cite web|url=https://www.worldscientific.com/page/rmp/editorial-board|title=Editorial Board - Founding editor|website=World Scientific|access-date=20 February 2021}} In 2012 he became a fellow of the American Mathematical Society.{{cite web|url=https://www.ams.org/cgi-bin/fellows/fellows.cgi|title=List of Fellows of the American Mathematical Society|website=American Mathematical Society|access-date=19 February 2021}} {{cite journal|last=Jackson|first=Allyn|title=Fellows of the AMS: Inaugural Class|journal=Notices of the AMS|volume=60|number=5|year=2013|pages=631–637|url=https://www.ams.org/profession/ams-fellows/rnoti-p631.pdf}}

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• {{cite book|last=Araki|first=Huzihiro|date=1999|title=Mathematical theory of quantum fields|volume=101|publisher=Oxford University Press on Demand|isbn=978-0199566402}}
• {{cite journal|last1=Araki|first1=Huzihiro|last2=Lieb|first2=Elliott H.|title=Entropy inequalities|journal=Communications in Mathematical Physics|volume=18|pages=160–170|year=1970|issue=2|doi=10.1007/BF01646092|bibcode=1970CMaPh..18..160A|s2cid=189832417|url=https://projecteuclid.org/euclid.cmp/1103842506}}
• {{cite journal|last1=Araki|first1=Huzihiro|last2=Woods|first2=E. J.|title=Representations of the canonical commutation relations describing a nonrelativistic infinite free Bose gas|journal=Journal of Mathematical Physics|volume=4|number=5|pages=637–662|year=1963|doi=10.1063/1.1704002|bibcode=1963JMP.....4..637A}}
• {{cite journal|last1=Araki|first1=Huzihiro|last2=Woods|first2=E. J.|title=A classification of factors|journal=Publications of the Research Institute for Mathematical Sciences, Kyoto University. Ser. A|volume=4|number=1|pages=51–130|year=1968|doi=10.2977/prims/1195195263|doi-access=free}}
• {{cite journal|last=Araki|first=Huzihiro|title=Relative Entropy of States of Von Neumann Algebras|journal=Publications of the Research Institute for Mathematical Sciences|pages=809–833|year=1976}}
• {{cite journal|last1=Araki|first1=Huzihiro|last2=Yanase|first2=Mutsuo M.|title=Measurement of Quantum Mechanical Operators|journal=Physical Review|volume=120|pages=622–626|year=1960|issue=2|doi=10.1103/PhysRev.120.622|bibcode=1960PhRv..120..622A}}
• {{cite journal|last1=Araki|first1=Huzihiro|last2=Hepp|first2=Klaus|last3=Ruelle|first3=David|title=On the asymptotic behaviour of Wightman functions in space-like directions|journal=Helvetica Physica Acta|volume=35|number=3|pages=164–174|year=1962|doi=10.5169/seals-113273}}
• {{cite journal|last=Araki|first=Huzihiro|title=On the equivalence of the KMS condition and the variational principle for quantum lattice systems|journal=Communications in Mathematical Physics|volume=38|pages=1–10|year=1974|issue=1|doi=10.1007/BF01651545|bibcode=1974CMaPh..38....1A|s2cid=73547157|url=https://projecteuclid.org/euclid.cmp/1103859514}}

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{{Portal|Mathematics|Physics|Biography}}

{{cols|colwidth=21em}}

• Araki–Sucher correction
• Algebraic quantum field theory
• C*-algebra
• KMS state
• Local quantum physics
• Quantum field theory
• Quantum thermodynamics
• Von Neumann algebra

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• {{Cite journal|last=Leong|first=Y. K.|title = Interview with Huzihiro Araki: Mathematics and Physics, A Tale of Two Cultures|journal=Asia Pacific Mathematics Newsletter|volume=4|number=2|pages=12–18|date=April 2014|url=https://www.asiapacific-mathnews.com/04/0402/0012_0018.pdf}}
• {{Cite journal|last=Valentin|first=Zagrebnov|title = Professor Huzihiro Araki about the IAMP|journal=IAMP News Bulletin|pages=10–13|date=April 2010|url=http://www.iamp.org/bulletins/old-bulletins/201004.pdf}}
• {{Cite journal|last1=Connes|first1=Alain|last2=Flato|first2=Moshé|last3=Hironaka|first3=Heisuke|last4=Jaffe|first4=Arthur|last5=Jones|first5=Vaughan|title = Editorial (dedication of this issue to Huzihiro Araki)|journal=Communications in Mathematical Physics|volume=155|pages=1–2|year=1993|issue=1|doi=10.1007/BF02100046|url=https://projecteuclid.org/euclid.cmp/1104253196}}
• {{cite web|url=http://www.iamp.org/poincare/ha03-laud.pdf|title=Longo's Laudatio for Araki's Poincare Prize|website=International Association of Mathematical Physics|access-date=20 February 2021}}

• {{mathgenealogy|35147}}
• {{DNB-Portal|134152417}}.
• {{zbMATH|id=huzihiro.araki}}.
• {{cite web|url=https://www.math.mcgill.ca/~jaksic/video.html|title=Araki's Lecture: Interaction between the modular theory of operator algebras and statistical physics - past, present (and future)|website=math.mcgill.ca|access-date=26 February 2021}}

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Category:20th-century Japanese physicists

Category:20th-century Japanese mathematicians

Category:21st-century Japanese mathematicians

Category:1932 births

Category:2022 deaths

Category:Kyoto University alumni

Category:Princeton University alumni

Category:Academic staff of Kyoto University

Category:Fellows of the American Mathematical Society

Category:Japanese mathematical physicists

Category:Presidents of the International Association of Mathematical Physics

Category:Scientists from Tokyo Metropolis