Rudolf Haag

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Rudolf Haag
Haag color 300 dpi v003 jpg.jpg
Rudolf Haag in 1992
Born(1922-08-17)17 August 1922
Died5 January 2016(2016-01-05) (aged 93)
Alma mater
Known for
Scientific career
ThesisDie korrespondenzmäßige Methode in der Theorie der Elementarteilchen (1951)
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. He was one of the founders of the modern formulation of quantum field theory and he identified the formal structure in terms of the principle of locality and local observables. He also made important advances in the foundations of quantum statistical mechanics.[2]


Rudolf Haag was born on 17 August 1922, in Tübingen, a university town in the middle of Baden-Württemberg. His family belonged to the cultured middle class. Haag's mother was the writer and politician Anna Haag.[3] His father, Albert Haag, was a teacher of mathematics at a Gymnasium. After finishing high-school in 1939, he visited his sister in London shortly before the beginning of World War II. He was interned as an enemy alien and spent the war in a camp of German civilians in Manitoba. There he used his spare-time after the daily compulsory labour to study physics and mathematics as an autodidact.[4]

After the war, Haag returned to Germany and enrolled at the Technical University of Stuttgart in 1946, 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[5] and became his assistant until 1956. In April 1953, he joined the CERN theoretical study group in Copenhagen[note 1] directed by Niels Bohr.[7][8] After a year, he returned to his assistant position in Munich and completed the German habilitation in 1954.[9] From 1956 to 1957 he worked with Werner Heisenberg at the Max Planck Institute for Physics in Göttingen.[10]

From 1957 to 1959, he was a visiting professor at Princeton University and from 1959 to 1960 he worked at the University of Marseille. He became a professor of Physics at the University of Illinois Urbana-Champaign in 1960. In 1965, he and Res Jost founded the journal Communications in Mathematical Physics. Haag remained the first editor-in-chief until 1973.[11] In 1966, he accepted the professorship position for theoretical physics at the University of Hamburg, where he stayed until he retired in 1987.[12] After retirement, he worked on the concept of the quantum physical event.[13]

Haag developed an interest in music at an early age. He began learning the violin, but later preferred the piano, which he played almost every day. In 1948, Haag married Käthe Fues,[note 2] with whom he had four children, Albert, Friedrich, Elisabeth, and Ulrich. After retirement, he moved together with his second wife Barbara Klie[note 3] to Schliersee, a pastoral village in the Bavarian mountains. He died on 5 January 2016, in Fischhausen-Neuhaus, in southern Bavaria.[15]

Scientific career[edit]

At the beginning of his career, Haag contributed significantly to the concepts of quantum field theory, including Haag's theorem, from which follows that the interaction picture of quantum mechanics does not exist in quantum field theory.[note 4] A new approach to the description of scattering processes of particles became necessary. In the following years Haag developed what is known as Haag–Ruelle scattering theory.[17]

During this work, he realized that the rigid relationship between fields and particles that had been postulated up to that point, did not exist, and that the particle interpretation should be based on Albert Einstein's principle of locality, which assigns operators to regions of spacetime. These insights found their final formulation in the Haag–Kastler axioms for local observables of quantum field theories.[18] This framework uses elements of the theory of operator algebras and is therefore referred to as algebraic quantum field theory or, from the physical point of view, as local quantum physics.[19]

This concept proved fruitful for understanding the fundamental properties of any theory in four-dimensional Minkowski space. Without making assumptions about non-observable charge-changing fields, Haag, in collaboration with Sergio Doplicher and John E. Roberts, elucidated the possible structure of the superselection sectors of the observables in theories with short-range forces.[note 5] Sectors can always be composes with one another, each sector satisfies either 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. In the special case of simple sectors, a global gauge group and charge-carrying fields, which can generate all sectors from the vacuum state, were reconstructed from the observables.[20][21] These results were later generalized for arbitrary sectors in the Doplicher–Roberts duality theorem.[22] 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.[23]

In quantum statistical mechanics, Haag, together with Nicolaas M. Hugenholtz and Marius Winnink, succeeded in generalizing the Gibbsvon Neumann characterization of thermal equilibrium states using the KMS condition (named after Ryogo Kubo, Paul C. Martin, and Julian Schwinger) in such a way that it extends to infinite systems in the thermodynamic limit. It turned out that this condition also plays a prominent role in the theory of von Neumann algebras and resulted in the Tomita–Takesaki theory. This theory has proven to be a central element in structural analysis and recently[note 6] also in the construction of concrete quantum field theoretical models.[note 7] Together with Daniel Kastler and Ewa Trych-Pohlmeyer, Haag also succeeded in deriving the KMS condition from the stability properties of thermal equilibrium states.[26] Together with Huzihiro Araki, Daniel Kastler, and Masamichi Takesaki, he also developed a theory of chemical potential in this context.[27]

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 and Hawking radiation.[28]

Haag had a certain mistrust towards what he viewed as speculative developments in theoretical physics[7] but occasionally dealt with such questions. The best known contribution is the Haag–Łopuszański–Sohnius theorem, which classifies the possible supersymmetries of the S-matrix that are not covered by the Coleman–Mandula theorem.[note 8][29]

Honors and awards[edit]

In 1970 Haag received the Max Planck Medal for outstanding achievements in theoretical physics[30] and in 1997 the Henri Poincaré Prize[31] for his fundamental contributions to quantum field theory as one of the founders of the modern formulation.[2] Since 1980 Haag was a member of the German National Academy of Sciences Leopoldina[32] and since 1981 of the Göttingen Academy of Sciences.[33] Since 1979 he was a corresponding member of the Bavarian Academy of Sciences[34] and since 1987 of the Austrian Academy of Sciences.[35]



  • 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.

Selected scientific works[edit]


See also[edit]


  1. ^ Since the laboratory in Geneva was still under construction, the study group was hosted by the Niels Bohr Institute in Copenhagen.[6]
  2. ^ Käthe Fues was one of the daughters of the German theoretical physicist Erwin Fues.[14]
  3. ^ Haag married Barbara Klie after Käthe's premature death.
  4. ^ 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.[16]
  5. ^ 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.
  6. ^ 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.[24]
  7. ^ An overview of the construction of a large number of models using these methods can be found in Lechner's chapter.[25]
  8. ^ 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.


  1. ^ Rudolf Haag (13 January 2016); Buchholz, Detlev; Fredenhagen, Klaus (2016). "Nachruf auf Rudolf Haag". Physik Journal (in German). 15 (4): 53. (Obituaries).
  2. ^ a b "Henri Poincaré Prize citation". International Association of Mathematical Physics. Retrieved 9 January 2021.
  3. ^ Haag, Rudolf; Haag, Anna (2003). Leben und gelebt werden: Erinnerungen und Betrachtungen (in German) (1 ed.). Silberburg. ISBN 978-3874075626. Timms, Edward (2016). Anna Haag and her Secret Diary of the Second World War: A Democratic German Feminist's Response to the Catastrophe of National Socialism. Peter Lang AG, Internationaler Verlag der Wissenschaften. ISBN 978-3034318181.
  4. ^ Kastler, Daniel (2003). "Rudolf Haag – Eighty years". Communications in Mathematical Physics. 237 (1–2): 3–6. Bibcode:2003CMaPh.237....3K. doi:10.1007/s00220-003-0829-1. S2CID 121438414.
  5. ^ The doctoral thesis is Haag, Rudolf (1951). Die korrespondenzmässige Methode in der Theorie der Elementarteilchen (Thesis) (in German). Munich.
  6. ^ Poggendorff, Johann C. (1958). J.C. Poggendorffs biographisch-literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften (in German). J.A. Barth.
  7. ^ a b Haag, Rudolf (2010). "Some people and some problems met in half a century of commitment to mathematical physics". The European Physical Journal H. 35 (3): 263–307. Bibcode:2010EPJH...35..263H. doi:10.1140/epjh/e2010-10032-4. S2CID 59320730.
  8. ^ "Closure of CERN's Theoretical Study Division in Copenhagen". Retrieved 19 January 2021.
  9. ^ The habilitation thesis is Haag, Rudolf (1954). On Quantum field theories (Thesis). Vol. 29. Copenaghen: Munksgaard in Komm. (published 1955).
  10. ^ Buchholz, Detlev; Fredenhagen, Klaus (2016). "Nachruf auf Rudolf Haag". Physik Journal (in German). 15 (4): 53.
  11. ^ Jaffe, Arthur; Rehren, Karl-Henning (2016). "Rudolf Haag". Physics Today. 69 (7): 70–71. Bibcode:2016PhT....69g..70J. doi:10.1063/PT.3.3244.
  12. ^ 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. S2CID 188592087.
  13. ^ Haag, Rudolf (1990). "Fundamental Irreversibility and the Concept of Events". Communications in Mathematical Physics. 132 (1): 245–252. Bibcode:1990CMaPh.132..245H. doi:10.1007/BF02278010. S2CID 120715539. Haag, Rudolf (2015). "Faces of Quantum Physics". The Message of Quantum Science. Lecture Notes in Physics. Vol. 899. 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): 1950037–1–9. Bibcode:2019IJQI...1750037H. doi:10.1142/S0219749919500370.
  14. ^ "Das Jahr 1958 Letzte Zusammenarbeit mit Heisenberg. Die Spinortheorie der Elementarteilchen und die Genfer Hochenergiekonferenz". Wolfgang Pauli. Sources in the History of Mathematics and Physical Sciences (in German). Vol. 18. Springer, Berlin, Heidelberg. 2005. p. 1186. doi:10.1007/3-540-26832-4_2. ISBN 978-3-540-26832-1.
  15. ^ Buchholz, Detlev; Doplicher, Sergio; Fredenhagen, Klaus (2016). "Rudolf Haag (1922 - 2016)" (PDF). News Bulletin, International Association of Mathematical Physics: 27–31.
  16. ^ "Haag theorem". Encyclopedia of Mathematics. Retrieved 9 January 2021.
  17. ^ 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. S2CID 16258638.
  18. ^ Brunetti, Romeo; Fredenhagen, Klaus (2006). "Algebraic Approach to Quantum Field Theory". Encyclopedia of Mathematical Physics. Academic Press. pp. 198–204. arXiv:math-ph/0411072. doi:10.1016/B0-12-512666-2/00078-X. ISBN 978-0-12-512666-3. S2CID 119018200.
  19. ^ 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.
  20. ^ Fredenhagen, Klaus (2015). "An Introduction to Algebraic Quantum Field Theory". Advances in Algebraic Quantum Field Theory. Mathematical Physics Studies. Springer International Publishing. pp. 1–30. doi:10.1007/978-3-319-21353-8_1. ISBN 978-3-319-21352-1.
  21. ^ Doplicher, Sergio; Haag, Rudolf; Roberts, John E. (1969). "Fields, observables and gauge transformations I". Communications in Mathematical Physics. 13 (1): 1–23. Bibcode:1969CMaPh..13....1D. doi:10.1007/BF01645267. S2CID 123420887. Doplicher, Sergio; Haag, Rudolf; Roberts, John E. (1969). "Fields, observables and gauge transformations II". Communications in Mathematical Physics. 15 (3): 173–200. Bibcode:1969CMaPh..15..173D. doi:10.1007/BF01645674. S2CID 189831020.
  22. ^ Doplicher, Sergio; Roberts, John E. (1989). "A new duality theory for compact groups". Inventiones Mathematicae. 98: 157–218. Bibcode:1989InMat..98..157D. doi:10.1007/BF01388849. S2CID 120280418. Doplicher, Sergio; Roberts, John E. (1990). "Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics". Communications in Mathematical Physics. 131 (1): 51–107. Bibcode:1990CMaPh.131...51D. doi:10.1007/BF02097680. S2CID 121071316.
  23. ^ Fredenhagen, Klaus; Rehren, Karl-Henning; Schroer, Bert (1989). "Superselection Sectors with Braid Group Statistics and Exchange Algebras. 1. General Theory". Communications in Mathematical Physics. 125 (2): 201. Bibcode:1989CMaPh.125..201F. doi:10.1007/BF01217906. S2CID 122633954. Fredenhagen, Klaus; Rehren, Karl-Henning; Schroer, Bert (1992). "Superselection sectors with braid group statistics and exchange algebras. 2. Geometric aspects and conformal covariance". Reviews in Mathematical Physics. 4: 113–157. Bibcode:1992RvMaP...4S.113F. doi:10.1142/S0129055X92000170. Froehlich, Juerg; Gabbiani, Fabrizio (1991). "Braid statistics in local quantum theory". Reviews in Mathematical Physics. 2 (3): 251–354. doi:10.1142/S0129055X90000107.
  24. ^ Summers, Stephen. "Constructive Quantum Field Theory". Department of Mathematics, University of Florida. Retrieved 9 January 2021.
  25. ^ Lechner, Gandalf (2015). "Algebraic Constructive Quantum Field Theory: Integrable Models and Deformation Techniques". Advances in Algebraic Quantum Field Theory. Mathematical Physics Studies. Springer International Publishing. pp. 397–448. doi:10.1007/978-3-319-21353-8. ISBN 978-3-319-21352-1.
  26. ^ Jäkel, Christian D. (2006). "Thermal Quantum Field Theory". Encyclopedia of Mathematical Physics. Academic Press. pp. 227–235. doi:10.1016/B0-12-512666-2/00089-4. ISBN 978-0-12-512666-3.
  27. ^ Longo, Roberto (2001). "Notes for a quantum index theorem". Communications in Mathematical Physics. 222 (1): 45–96. arXiv:math/0003082. Bibcode:2001CMaPh.222...45L. doi:10.1007/s002200100492. S2CID 14305468.
  28. ^ Kay, Bernard S. (2006). "Quantum Field Theory in Curved Spacetime". Encyclopedia of Mathematical Physics. Academic Press. pp. 202–212. arXiv:gr-qc/0601008. doi:10.1016/B0-12-512666-2/00018-3. ISBN 978-0-12-512666-3. S2CID 16258638.
  29. ^ Maldacena, Juan Martin (1998). "The Large N limit of superconformal field theories and supergravity". Advances in Theoretical and Mathematical Physics. 2 (4): 231–252. arXiv:hep-th/9711200. doi:10.1023/A:1026654312961. S2CID 12613310. Martin, Stephen P. (2010). "A Supersymmetry Primer". Perspectives on Supersymmetry II. Advanced Series on Directions in High Energy Physics. Vol. 21. pp. 1–153. arXiv:hep-ph/9709356. doi:10.1142/9789814307505_0001. ISBN 978-981-4307-48-2.
  30. ^ "Max Planck Medal Prize winners". German Physical Society (in German). Retrieved 9 January 2021.
  31. ^ "Henri Poincaré Prize winners". International Association of Mathematical Physics. Retrieved 9 January 2021.
  32. ^ "German National Academy of Sciences Leopoldina member page of Rudolf Haag". German National Academy of Sciences Leopoldina. Retrieved 9 January 2021.
  33. ^ "Göttingen Academy of Sciences member page of Rudolf Haag". Göttingen Academy of Sciences (in German). Retrieved 3 March 2021. (:Unkn) Unknown (2011). Akademie der Wissenschaften zu Göttingen (ed.). Jahrbuch der Akademie der Wissenschaften zu Göttingen 2010 (in German). De Gruyter. doi:10.26015/adwdocs-386. ISBN 978-3110236767.
  34. ^ "Bavarian Academy of Sciences member page of Rudolf Haag". Bavarian Academy of Sciences. Retrieved 9 January 2021.
  35. ^ "Austrian Academy of Sciences member page of Rudolf Haag". Austrian Academy of Sciences. Retrieved 9 January 2021.

Further reading[edit]

External links[edit]