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== Biography ==
== Biography ==
Haag's father, Albert Haag, was a Gymnasium teacher in mathematics. His mother was the writer and politician Anna Haag. Haag stayed in England at the beginning of [[World War II]] and was [[Internment|interned]] as an [[enemy alien]] in Canada, where he studied self-taught physics and mathematics<ref>{{Cite journal|last = Kastler|first = Daniel|title = Rudolf Haag – Eighty years|journal = Communications in Mathematical Physics|volume = 237|pages = 3–6|year = 2003|doi = 10.1007/s00220-003-0829-1}}</ref>. From 1946, he studied at the [[University of Stuttgart|Technical University in Stuttgart]], where he graduated as a physicist in 1948. In 1951 he received his doctorate at the [[Ludwig Maximilian University of Munich|University of Munich]] under the supervision of [[Fritz Bopp]]<ref>The doctoral thesis is {{cite thesis|last=Haag|first=Rudolf|date=1951|title=Die korrespondenzmässige Methode in der Theorie der Elementarteilchen|lang=de|url=https://opac.ub.uni-muenchen.de/TouchPoint/perma.do?q=+0%3D%225363125%22+IN+%5B2%5D&l=en|place=Munich}}</ref> and completed his [[habilitation]] in 1954<ref>The habilitation thesis is {{cite thesis|last=Haag|first=Rudolf|date=1954|publication-date=1955|title=On Quantum field theories|lang=en|volume=29|number=12|publisher=Munksgaard in Komm.|url=https://opac.ub.uni-muenchen.de/TouchPoint/perma.do?q=+0%3D%225874215%22+IN+%5B2%5D&l=en|place=Copenaghen}}</ref>. From 1951 to 1956, he was an assistant at the University of Munich (from 1954 as a private lecturer) and in 1953/54 he attended the theory group at [[CERN]], which at that time was still based in [[Copenhagen]]<ref>{{Cite book|last = Poggendorff|first = Johann C.|date = 1958|title = J.C. Poggendorffs biographisch-literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften|publisher = J.A. Barth|lang=de}}</ref>. In 1956/1957, he worked with [[Werner Heisenberg]] at the [[Max Planck Institute for Physics]] in [[Göttingen]]. After being a visiting professor at [[Princeton University]] and at the [[Aix-Marseille University|University of Marseille]], he became professor of Physics at the [[University of Illinois at Urbana-Champaign|University of Illinois in Urbana-Champaign]]. Afterwards, he was professor for theoretical physics at the [[Universität Hamburg]] until his retirement in 1987<ref>{{Cite journal|last1 = Buchholz|first1 = Detlev|last2 = Doplicher|first2 = Sergio|last3 = Fredenhagen|first3 = Klaus|title = Rudolf Haag (1922–2016)|journal = News Bulletin, International Association of Mathematical Physics|pages = 27–31|year = 2016|url = http://www.iamp.org/bulletins/old-bulletins/Bulletin-January2016-print.pdf}}</ref>. After his retirement, he moved to the [[Schliersee (lake)| Schliersee]]<ref>{{Cite journal|last1 = Schönhammer|first1 = Kurt|title = Nachruf auf Rudolf Haag. 17. August 1922 – 5. Januar 2016|journal = Jahrbuch der Akademie der Wissenschaften zu Göttingen|pages = 236–237|year = 2016|lang = de|doi = 10.1515/jbg-2016-0026}}</ref>, where he worked on the concept of events in quantum physics<ref>{{Cite journal|last = Haag|first = Rudolf|title = Fundamental Irreversability and the Concept of Events|journal = Communications in Mathematical Physics|volume = 132|pages = 245–252|year = 1990|doi = 10.1007/BF02278010|url = https://lib-extopc.kek.jp/preprints/PDF/1990/9007/9007060.pdf}}</ref> until his death.
Haag's father, Albert Haag, was a Gymnasium teacher in mathematics. His mother was the writer and politician Anna Haag. Haag stayed in England at the beginning of [[World War II]] and was [[Internment|interned]] as an [[enemy alien]] in Canada, where he studied self-taught physics and mathematics<ref>{{Cite journal|last = Kastler|first = Daniel|title = Rudolf Haag – Eighty years|journal = Communications in Mathematical Physics|volume = 237|pages = 3–6|year = 2003|doi = 10.1007/s00220-003-0829-1}}</ref>. From 1946, he studied at the [[University of Stuttgart|Technical University in Stuttgart]], where he graduated as a physicist in 1948. In 1951 he received his doctorate at the [[Ludwig Maximilian University of Munich|University of Munich]] under the supervision of [[Fritz Bopp]]<ref>The doctoral thesis is {{cite thesis|last=Haag|first=Rudolf|date=1951|title=Die korrespondenzmässige Methode in der Theorie der Elementarteilchen|lang=de|url=https://opac.ub.uni-muenchen.de/TouchPoint/perma.do?q=+0%3D%225363125%22+IN+%5B2%5D&l=en|place=Munich}}</ref> and completed his [[habilitation]] in 1954<ref>The habilitation thesis is {{cite thesis|last=Haag|first=Rudolf|date=1954|publication-date=1955|title=On Quantum field theories|lang=en|volume=29|number=12|publisher=Munksgaard in Komm.|url=https://opac.ub.uni-muenchen.de/TouchPoint/perma.do?q=+0%3D%225874215%22+IN+%5B2%5D&l=en|place=Copenaghen}}</ref>. From 1951 to 1956, he was an assistant at the University of Munich (from 1954 as a private lecturer) and in 1953/54 he attended the theory group at [[CERN]], which at that time was still based in [[Copenhagen]]<ref>{{Cite book|last = Poggendorff|first = Johann C.|date = 1958|title = J.C. Poggendorffs biographisch-literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften|publisher = J.A. Barth|lang=de}}</ref>. In 1956/1957, he worked with [[Werner Heisenberg]] at the [[Max Planck Institute for Physics]] in [[Göttingen]]. After being a visiting professor at [[Princeton University]] and at the [[Aix-Marseille University|University of Marseille]], he became professor of Physics at the [[University of Illinois at Urbana-Champaign|University of Illinois in Urbana-Champaign]]. Afterwards, he was professor for theoretical physics at the [[Universität Hamburg]] until his retirement in 1987<ref>{{Cite journal|last1 = Buchholz|first1 = Detlev|last2 = Doplicher|first2 = Sergio|last3 = Fredenhagen|first3 = Klaus|title = Rudolf Haag (1922–2016)|journal = News Bulletin, International Association of Mathematical Physics|pages = 27–31|year = 2016|url = http://www.iamp.org/bulletins/old-bulletins/Bulletin-January2016-print.pdf}}</ref>. After his retirement, he moved to the [[Schliersee (lake)| Schliersee]]<ref>{{Cite journal|last1 = Schönhammer|first1 = Kurt|title = Nachruf auf Rudolf Haag. 17. August 1922 – 5. Januar 2016|journal = Jahrbuch der Akademie der Wissenschaften zu Göttingen|pages = 236–237|year = 2016|lang = de|doi = 10.1515/jbg-2016-0026}}</ref>, where he worked on the concept of events in quantum physics<ref>{{Cite journal|last = Haag|first = Rudolf|title = Fundamental Irreversability and the Concept of Events|journal = Communications in Mathematical Physics|volume = 132|pages = 245–252|year = 1990|doi = 10.1007/BF02278010|url = https://lib-extopc.kek.jp/preprints/PDF/1990/9007/9007060.pdf}} {{Cite book|last=Haag|first=Rudolf|date=2015|chapter=Faces of Quantum Physics|title=The Message of Quantum Science|pages=219–234|publisher=Springer, Berlin, Heidelberg|isbn=978-3-662-46422-9|doi=10.1007/978-3-662-46422-9_9}} {{Cite journal|last=Haag|first=Rudolf|title=On quantum theory|journal=International Journal of Quantum Information|volume=17|number=4|year=2019|doi=10.1142/S0219749919500370}} </ref> until his death.


Together with [[Res Jost]], Haag was the founder and, from 1965 to 1973, the first editor of the leading journal ''[[Communications in Mathematical Physics]]''<ref>{{Cite journal|last1 = Jaffe|first1 = Arthur|last2 = Rehren|first2 = Karl-Henning|title = Rudolf Haag|journal = Physics Today|pages = 70–71|year = 2016|doi = 10.1063/PT.3.3244}}</ref>.
Together with [[Res Jost]], Haag was the founder and, from 1965 to 1973, the first editor of the leading journal ''[[Communications in Mathematical Physics]]''<ref>{{Cite journal|last1 = Jaffe|first1 = Arthur|last2 = Rehren|first2 = Karl-Henning|title = Rudolf Haag|journal = Physics Today|pages = 70–71|year = 2016|doi = 10.1063/PT.3.3244}}</ref>.
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|doi = 10.1007/BF02278010
|doi = 10.1007/BF02278010
|url = https://lib-extopc.kek.jp/preprints/PDF/1990/9007/9007060.pdf
|url = https://lib-extopc.kek.jp/preprints/PDF/1990/9007/9007060.pdf
}} (Concept of Event; see also Section VII.3 in the following book).
}} (Concept of event; see also Section VII.3 in the following book).
* {{Cite book
* {{Cite book
|last = Haag
|last = Haag
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|year = 2010
|year = 2010
|doi = 10.1140/epjh/e2010-10042-7
|doi = 10.1140/epjh/e2010-10042-7
}} (Personal memories and outlook).
}} (Personal memories).
*{{Cite book
|last = Haag
|first = Rudolf
|date = 2015
|chapter = Faces of Quantum Physics
|title = The Message of Quantum Science
|pages = 219–234
|publisher = Springer, Berlin, Heidelberg
|isbn = 978-3-662-46422-9
|doi = 10.1007/978-3-662-46422-9_9
}} (Review and concept of event).
*{{Cite journal
|last = Haag
|first = Rudolf
|title = On quantum theory
|journal = International Journal of Quantum Information
|volume = 17
|number = 4
|year = 2019
|doi = 10.1142/S0219749919500370
}} (Quantum ontology and concept of event).
{{div col end}}
{{div col end}}


Revision as of 13:35, 16 November 2020

Rudolf Haag
Born(1922-08-17)17 August 1922
Tübingen, Germany
Died5 January 2016(2016-01-05) (aged 93)
Neuhaus (Schliersee), Germany[1]
Alma materUniversity of Stuttgart
Known for
Awards
Scientific career
FieldsPhysics
Institutions
Thesis Die korrespondenzmäßige Methode in der Theorie der Elementarteilchen
Doctoral advisorFritz Bopp
Doctoral students

Rudolf Haag (17 August 1922 – 5 January 2016) was a German theoretical physicist, who mainly dealt with fundamental questions of quantum field theory.

Biography

Haag's father, Albert Haag, was a Gymnasium teacher in mathematics. His mother was the writer and politician Anna Haag. Haag stayed in England at the beginning of World War II and was interned as an enemy alien in Canada, where he studied self-taught physics and mathematics[2]. From 1946, he studied at the Technical University in Stuttgart, where he graduated as a physicist in 1948. In 1951 he received his doctorate at the University of Munich under the supervision of Fritz Bopp[3] and completed his habilitation in 1954[4]. From 1951 to 1956, he was an assistant at the University of Munich (from 1954 as a private lecturer) and in 1953/54 he attended the theory group at CERN, which at that time was still based in Copenhagen[5]. In 1956/1957, he worked with Werner Heisenberg at the Max Planck Institute for Physics in Göttingen. After being a visiting professor at Princeton University and at the University of Marseille, he became professor of Physics at the University of Illinois in Urbana-Champaign. Afterwards, he was professor for theoretical physics at the Universität Hamburg until his retirement in 1987[6]. After his retirement, he moved to the Schliersee[7], where he worked on the concept of events in quantum physics[8] until his death.

Together with Res Jost, Haag was the founder and, from 1965 to 1973, the first editor of the leading journal Communications in Mathematical Physics[9].

Among his students are[10]: Huzihiro Araki, Detlev Buchholz, Volker Enß, Klaus Fredenhagen, and Bert Schroer.

Academic career

Even at the beginning of his career, Haag contributed significantly to the concepts of quantum field theory, including Haag's theorem[11]. From this theorem it follows that the interaction picture of quantum mechanics does not exist in quantum field theory[12]. Therefore, a new approach to the description of the scattering processes of particles was necessary, which he developed in the following years (Haag-Ruelle scattering theory[13]).

During this work, he realized that the rigid relationship between fields and particles that had been postulated up to that point did not exist. The decisive factor for the particle interpretation is rather the Einstein locality principle, transferred to quantum field theory, which assigns operators to regions of spacetime. These insights found their final formulation in the Haag-Kastler axioms for the local observables of every quantum field theory[14]. This framework uses elements of the theory of operator algebras and is therefore referred to as algebraic quantum field theory or, with a view to the physical content, as local quantum physics[15].

This concept proved fruitful for understanding fundamental properties of any theory in four-dimensional Minkowski space. Without making assumptions about the existence of fields that are not directly observable (since they change the charge), Haag, in collaboration with Sergio Doplicher and John E. Roberts, has elucidated the possible structure of the superselection sectors of the observables in theories with short-range forces[16]. Sectors can always compose, each sector satisfies either the para-Bose or para-Fermi statistics and for each sector there is a conjugate sector. These insights correspond to the additivity of charges in the particle interpretation, to the Bose-Fermi alternative for particle statistics and to the existence of antiparticles[17]. In a special case (simple sectors) a global gauge group and charge-carrying fields could be reconstructed from the observables, the charged fields generate all sectors from the vacuum state. These results were later generalized for arbitrary sectors by Doplicher and Roberts (Doplicher-Roberts duality theorem). The application of these methods to theories in low-dimensional spaces also led to an understanding of the occurrence of braid group statistics and Quantum groups.

In quantum statistical mechanics, Haag, together with Nicolaas M. Hugenholtz and Marius Winnink, succeeded in generalizing the Gibbs-von Neumann characterization of thermal equilibrium states using the KMS condition (from Kubo, Martin, and Schwinger) in such a way that it also extends to infinite systems in the thermodynamic limit[18]. It turned out that this condition also plays a prominent role in the theory of von Neumann algebras (Tomita–Takesaki theory). This theory has proven to be a central element in structural analysis and recently[19] also in the construction of concrete quantum field theoretical models[20]. Together with Daniel Kastler and Ewa Trych-Pohlmeyer, Haag also succeeded in deriving the KMS condition from the stability properties of thermal equilibrium states[21]. Together with Huzihiro Araki, Daniel Kastler and Masamichi Takesaki, he also developed a theory of chemical potential in this context[22].

The framework created by Haag and Kastler for studying quantum field theories in Minkowski space can be transferred to theories in curved spacetime. By working with Klaus Fredenhagen, Heide Narnhofer and Ulrich Stein, Haag made important contributions to the understanding of the Unruh effect[23] and Hawking radiation[24].

Haag had a certain mistrust towards what he saw as speculative developments in theoretical physics[25], but occasionally dealt with such questions. The best known is the Haag–Łopuszański–Sohnius theorem[26], which classifies the possible supersymmetries of the S-matrix that are not covered by the Coleman–Mandula theorem[27].

Honors and awards

In 1970 he received the Max Planck Medal[28] and in 1997 the Henri Poincaré Prize[29]. He was a member of the German National Academy of Sciences Leopoldina (since 1980)[30] and the Göttingen Academy of Sciences (since 1981)[31]. He was a corresponding member of the Bavarian Academy of Sciences (since 1979)[32] and of the Austrian Academy of Sciences (since 1987)[33].

Publications

  • Haag, Rudolf (1955). "On quantum field theories". Dan. Mat. Fys. Medd. 29N12: 1–37. (Haag's theorem).
  • Haag, Rudolf (1958). "Quantum field theories with composite particles and asymptotic conditions". Physical Review. 112: 669–673. doi:10.1103/PhysRev.112.669. (Haag–Ruelle scattering theory).
  • Haag, Rudolf; Kastler, Daniel (1964). "An Algebraic approach to quantum field theory". Journal of Mathematical Physics. 5: 848–861. doi:10.1063/1.1704187. (Haag–Kastler axioms).
  • Haag, Rudolf; Hugenholtz, Nico M.; Winnink, Marius (1967). "On the Equilibrium states in quantum statistical mechanics". Communications in Mathematical Physics. 5: 215–236. doi:10.1007/BF01646342. (KMS condition).
  • Doplicher, Sergio; Haag, Rudolf; Roberts, John E. (1971). "Local observables and particle statistics. 1". Communications in Mathematical Physics. 23: 199–230. doi:10.1007/BF01877742.
  • Doplicher, Sergio; Haag, Rudolf; Roberts, John E. (1974). "Local observables and particle statistics. 2". Communications in Mathematical Physics. 35: 49–85. doi:10.1007/BF01646454. (Doplicher-Haag-Roberts analysis of the Superselection structure).
  • Haag, Rudolf; Kastler, Daniel; Trych-Pohlmeyer, Ewa B. (1974). "Stability and equilibrium states". Communications in Mathematical Physics. 38: 173–193. doi:10.1007/BF01651541. (Stability and KMS condition).
  • Haag, Rudolf; Lopuszanski, Jan T.; Sohnius, Martin (1975). "All Possible Generators of Supersymmetries of the s Matrix". Nuclear Physics B. 88: 257. doi:10.1016/0550-3213(75)90279-5. (Classification of Supersymmetry).
  • Araki, Huzihiro; Kastler, Daniel; Takesaki, Masamichi; Haag, Rudolf (1977). "Extension of KMS States and Chemical Potential". Communications in Mathematical Physics. 53: 97–134. doi:10.1007/BF01609126. (KMS condition and chemical potential).
  • Haag, Rudolf; Narnhofer, Heide; Stein, Ulrich (1984). "On Quantum Field Theory in Gravitational Background". Communications in Mathematical Physics. 94: 219. doi:10.1007/BF01209302. (Unruh effect).
  • Fredenhagen, Klaus; Haag, Rudolf (1990). "On the Derivation of Hawking Radiation Associated With the Formation of a Black Hole" (PDF). Communications in Mathematical Physics. 127: 273. doi:10.1007/BF02096757. (Hawking radiation).
  • Haag, Rudolf (1990). "Fundamental Irreversability and the Concept of Events" (PDF). Communications in Mathematical Physics. 132: 245–252. doi:10.1007/BF02278010. (Concept of event; see also Section VII.3 in the following book).
  • Haag, Rudolf (1996). Local quantum physics: Fields, particles, algebras (2 ed.). Springer-Verlag Berlin Heidelberg. doi:10.1007/978-3-642-61458-3. ISBN 978-3-540-61049-6. (Textbook).
  • Buchholz, Detlev; Haag, Rudolf (2000). "The Quest for understanding in relativistic quantum physics". Journal of Mathematical Physics. 41: 3674–3697. arXiv:hep-th/9910243. doi:10.1063/1.533324. (Review and outlook).
  • Haag, Rudolf (2000). "Questions in quantum physics: A Personal view". Mathematical Physics 2000: 87–100. arXiv:hep-th/0001006. doi:10.1142/9781848160224_0005. (Outlook).
  • Haag, Rudolf (2010). "Some people and some problems met in half a century of commitment to mathematical physics". The European Physical Journal H. 35: 263–307. doi:10.1140/epjh/e2010-10032-4. (Personal memories).
  • Haag, Rudolf (2010). "Local algebras. A look back at the early years and at some achievements and missed opportunities". The European Physical Journal H. 35: 255–261. doi:10.1140/epjh/e2010-10042-7. (Personal memories).
  • Haag, Rudolf (2015). "Faces of Quantum Physics". The Message of Quantum Science. Springer, Berlin, Heidelberg. pp. 219–234. doi:10.1007/978-3-662-46422-9_9. ISBN 978-3-662-46422-9. (Review and concept of event).
  • Haag, Rudolf (2019). "On quantum theory". International Journal of Quantum Information. 17 (4). doi:10.1142/S0219749919500370. (Quantum ontology and concept of event).

References

  1. ^ Rudolf Haag (13 January 2016); Buchholz, Detlev; Fredenhagen, Klaus (2016). "Nachruf auf Rudolf Haag". Physik Journal (in German). 15 (4): 53. (Obituaries).
  2. ^ Kastler, Daniel (2003). "Rudolf Haag – Eighty years". Communications in Mathematical Physics. 237: 3–6. doi:10.1007/s00220-003-0829-1.
  3. ^ The doctoral thesis is Haag, Rudolf (1951). Die korrespondenzmässige Methode in der Theorie der Elementarteilchen (Thesis) (in German). Munich.
  4. ^ The habilitation thesis is Haag, Rudolf (1954). On Quantum field theories (Thesis). Vol. 29. Copenaghen: Munksgaard in Komm. (published 1955).
  5. ^ Poggendorff, Johann C. (1958). J.C. Poggendorffs biographisch-literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften (in German). J.A. Barth.
  6. ^ Buchholz, Detlev; Doplicher, Sergio; Fredenhagen, Klaus (2016). "Rudolf Haag (1922–2016)" (PDF). News Bulletin, International Association of Mathematical Physics: 27–31.
  7. ^ Schönhammer, Kurt (2016). "Nachruf auf Rudolf Haag. 17. August 1922 – 5. Januar 2016". Jahrbuch der Akademie der Wissenschaften zu Göttingen (in German): 236–237. doi:10.1515/jbg-2016-0026.
  8. ^ Haag, Rudolf (1990). "Fundamental Irreversability and the Concept of Events" (PDF). Communications in Mathematical Physics. 132: 245–252. doi:10.1007/BF02278010. Haag, Rudolf (2015). "Faces of Quantum Physics". The Message of Quantum Science. Springer, Berlin, Heidelberg. pp. 219–234. doi:10.1007/978-3-662-46422-9_9. ISBN 978-3-662-46422-9. Haag, Rudolf (2019). "On quantum theory". International Journal of Quantum Information. 17 (4). doi:10.1142/S0219749919500370.
  9. ^ Jaffe, Arthur; Rehren, Karl-Henning (2016). "Rudolf Haag". Physics Today: 70–71. doi:10.1063/PT.3.3244.
  10. ^ Rudolf Haag at the Mathematics Genealogy Project.
  11. ^ Haag's theorem states that the usual Fock space representation cannot be used to describe interacting relativistic quantum fields with canonical commutation relations. One needs inequivalent Hilbert space representations of fields; see also Encyclopedia of Mathematics.
  12. ^ Haag, Rudolf (1955). "On quantum field theories". Dan. Mat. Fys. Medd. 29N12: 1–37.
  13. ^ See e.g. the review: Buchholz, Detlev; Summers, Stephen J. (2006). "Scattering in Relativistic Quantum Field Theory: Fundamental Concepts and Tools". Encyclopedia of Mathematical Physics. Academic Press. pp. 456–465. arXiv:math-ph/0509047. doi:10.1016/B0-12-512666-2/00018-3. ISBN 978-0-12-512666-3.
  14. ^ Haag, Rudolf; Kastler, Daniel (1964). "An Algebraic approach to quantum field theory". Journal of Mathematical Physics. 5: 848–861. doi:10.1063/1.1704187.
  15. ^ Haag, Rudolf (1996). Local quantum physics: Fields, particles, algebras (2 ed.). Springer-Verlag Berlin Heidelberg. doi:10.1007/978-3-642-61458-3. ISBN 978-3-540-61049-6.
  16. ^ The only additional assumption to the Haag-Kastler axioms for the observables in this analysis was the postulate of the Haag duality, which was later established by Joseph J. Bisognano and Eyvind H. Wichmann in the framework of quantum field theory; the discussion of infinite statistics was also dispensed with.
  17. ^ Doplicher, Sergio; Haag, Rudolf; Roberts, John E. (1971). "Local observables and particle statistics. 1". Communications in Mathematical Physics. 23: 199–230. doi:10.1007/BF01877742.; Doplicher, Sergio; Haag, Rudolf; Roberts, John E. (1974). "Local observables and particle statistics. 2". Communications in Mathematical Physics. 35: 49–85. doi:10.1007/BF01646454.
  18. ^ Haag, Rudolf; Hugenholtz, Nico M.; Winnink, Marius (1967). "On the Equilibrium states in quantum statistical mechanics". Communications in Mathematical Physics. 5: 215–236. doi:10.1007/BF01646342.
  19. ^ It is referred to the algebraic constructive quantum field theories born at the beginning of this century. They are different respect to the constructive theories mathematically developed in the 70s and 80s inspired by semiclassical ideas. See for example Summers' historical overview.
  20. ^ An overview of the construction of a large number of models using these methods can be found in: Lechner, Gandalf (2015). "Algebraic Constructive Quantum Field Theory: Integrable Models and Deformation Techniques". Advances in Algebraic Quantum Field Theory. Springer International Publishing. pp. 397–448. doi:10.1007/978-3-319-21353-8. ISBN 978-3-319-21352-1.
  21. ^ Haag, Rudolf; Kastler, Daniel; Trych-Pohlmeyer, Ewa B. (1974). "Stability and equilibrium states". Communications in Mathematical Physics. 38: 173–193. doi:10.1007/BF01651541.
  22. ^ Araki, Huzihiro; Kastler, Daniel; Takesaki, Masamichi; Haag, Rudolf (1977). "Extension of KMS States and Chemical Potential". Communications in Mathematical Physics. 53: 97–134. doi:10.1007/BF01609126.
  23. ^ Haag, Rudolf; Narnhofer, Heide; Stein, Ulrich (1984). "On Quantum Field Theory in Gravitational Background". Communications in Mathematical Physics. 94: 219. doi:10.1007/BF01209302.
  24. ^ Fredenhagen, Klaus; Haag, Rudolf (1990). "On the Derivation of Hawking Radiation Associated With the Formation of a Black Hole" (PDF). Communications in Mathematical Physics. 127: 273. doi:10.1007/BF02096757.
  25. ^ Haag, Rudolf (2010). "Local algebras. A look back at the early years and at some achievements and missed opportunities". The European Physical Journal H. 35: 255–261. doi:10.1140/epjh/e2010-10042-7.
  26. ^ Haag, Rudolf; Lopuszanski, Jan T.; Sohnius, Martin (1975). "All Possible Generators of Supersymmetries of the s Matrix". Nuclear Physics B. 88: 257. doi:10.1016/0550-3213(75)90279-5.
  27. ^ The theorem of Sidney Coleman and Jeffrey Mandula excludes a nontrivial coupling of bosonic inner symmetry groups with geometric symmetries (Poincaré group). The supersymmetry, on the other hand, allows such a coupling.
  28. ^ https://www.dpg-physik.de/auszeichnungen/dpg-preise/max-planck-medaille/preistraeger.
  29. ^ http://www.iamp.org/page.php?page=page_prize_poincare.
  30. ^ https://www.leopoldina.org/en/members/list-of-members/list-of-members/member/Member/show/rudolf-haag/.
  31. ^ Akademie der Wissenschaften zu Göttingen, ed. (2011). Jahrbuch der Akademie der Wissenschaften zu Göttingen 2010 (in German). De Gruyter. doi:10.26015/adwdocs-386. ISBN 978-3110236767.
  32. ^ Bavarian Academy of Sciences members page of Rudolf Haag.
  33. ^ Austrian Academy of Sciences members page of Rudolf Haag.

Literature

External links

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