Rudolf Haag

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Rudolf Haag

Rudolf Haag (born August 17, 1922 in Tübingen ; † January 5, 2016 in Fischhausen-Neuhaus) was a German theoretical physicist who primarily dealt with fundamental questions of quantum field theory.

Life

Haag's father, Albert Haag, was a grammar school teacher for mathematics, his mother was the writer and politician Anna Haag . Haag stayed in England at the beginning of the Second World War and was interned as an Enemy Alien in Canada during the war , where he self-taught in physics and mathematics. 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 Fritz Bopp (The correspondence method in the theory of elementary particles) and qualified as a professor in 1954 (On the relativistic quantum theory of interacting particles) . From 1951 to 1953 he was an assistant at the University of Munich (from 1954 private lecturer) and in 1953/54 attended the theory group at CERN , which at that time was still based in Copenhagen . In 1956/1957 he worked with Werner Heisenberg at the Max Planck Institute for Physics in Göttingen . After visiting professorships at Princeton University and the Université de Marseille , he was Professor of Physics at the University of Illinois in Urbana-Champaign from 1960 to 1966 . Afterwards he was professor for theoretical physics at the University of Hamburg until his retirement in 1987 . After his retirement, he moved to Schliersee, where he worked on the concept of events in quantum physics until his death.

Haag was, together with Res Jost , founder and from 1965 to 1973 first editor of the leading journal for mathematical physics Communications in Mathematical Physics .

His students include a. Huzihiro Araki , Detlev Buchholz , Volker Enß , Klaus Fredenhagen and Bert Schroer .

Act

Even at the beginning of his career, Haag contributed significantly to the concepts of quantum field theory, including a. by Haag's theorem . From this theorem it follows that the interaction picture of quantum mechanics does not exist in quantum field theory. 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 .)

During this work, he recognized 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 , which is transferred to quantum field theory and which assigns operators to the areas of spacetime. These insights found their final formulation in the Haag-Kastler axioms for the local observables of every quantum field theory. 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 .

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 cannot be directly observed (since the charge changes), Haag, in collaboration with Sergio Doplicher and John E. Roberts , has elucidated the possible structure of the superselecting sectors of the observables in theories with short-range forces: Sectors can always be composed, each sector satisfies either the (para) Bose or the Fermist statistic and for each sector there is a conjugate sector. In the particle image, these insights correspond to the additivity of charges, the Bose-Fermi alternative for particle statistics and the existence of antiparticles . In a special case (simple sectors) a global calibration group and charge-carrying fields could be reconstructed from the observables , which 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 there .

In quantum statistical mechanics, Haag (together with Nico M. Hugenholtz and Marius Winnink ) succeeded in generalizing the Gibbs - von Neumann characterization of thermal equilibrium states using the KMS condition (according to Kubo , Martin , Schwinger ) in such a way that it also extends to infinity Systems in the thermodynamic Limes is applicable. 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 also in the construction of concrete quantum field theoretical models. Together with Daniel Kastler and Ewa Trych-Pohlmeyer, Haag also succeeded in deriving the KMS condition from the stability properties of thermal equilibrium states. Together with Huzihiro Araki, Daniel Kastler and Masamichi Takesaki , he also developed a theory of chemical potential in this context .

The framework created by Haag and Kastler for the treatment of quantum field theories in the 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 .

Haag exercised a certain reluctance towards what he saw as speculative developments in theoretical physics, but has occasionally dealt with such questions. The best known here is the Haag-Łopuszański-Sohnius theorem , which classifies the possible supersymmetries of the S matrix that are not covered by the Coleman-Mandula theorem .

Honors

In 1970 he received the Max Planck Medal and in 1997 the Henri Poincaré Prize . He was a member of the German Academy of Sciences Leopoldina (since 1980) and the Academy of Sciences in Göttingen and a corresponding member of the Bavarian Academy of Sciences and the Austrian Academy of Sciences .

Fonts

  • On quantum field theories , Matematisk-fysiske Meddelelser Kong. Danske Videns. Selskab, Vol. 29, 1955, No. 12 (Haagsche's theorem).
  • Quantum field theory with composite particles and asymptotic conditions . Physical Review , Vol. 112, 1958, 669 (Haag-Ruelle scattering theory).
  • with Daniel Kastler: An algebraic approach to quantum field theory . Journal of Mathematical Physics , Vol. 5, 1964, pp. 848-861 (Haag-Kastler-Axiome).
  • with Sergio Doplicher, Rudolf Haag, John E. Roberts: Local observables and particle statistics 1 & 2 . Commun.Math.Phys. 23 (1971) 199-230 & Commun. Math. Phys. 35 (1974) 49-85 (Doplicher-Haag-Roberts analysis of the superselect structure)
  • with Nico Hugenholtz, Marius Winnink: On the Equilibrium states in quantum statistical mechanics . Commun.Math.Phys. 5 (1967) 215-236 (KMS condition).
  • with Daniel Kastler, Ewa Trych-Pohlmeyer: Stability and equilibrium states . Commun.Math.Phys. 38 (1974) 173-193 (stability and KMS condition)
  • with Huzihiro Araki, Daniel Kastler, Masamichi Takesaki: Extension of KMS states and chemical potential . Commun. Math. Phys. 53 (1977) 97-134 (KMS condition and chemical potential)
  • with Heide Narnhofer, Ulrich Stein: On quantum field theory in gravitational background . Commun.Math.Phys. 94 (1984) 219 (balance wheel effect)
  • with Klaus Fredenhagen: On the derivation of Hawking radiation associated with the formation of a black hole . Commun.Math.Phys. 127 (1990) 273 (Hawking radiation)
  • with Jan Lopuszanski, Martin Sohnius: All possible generators of supersymmetries of the S matrix , Nucl. Phys, B 88 (1975) 257 (classification of supersymmetry)
  • Fundamental irreversibility and the concept of events , Commun.Math.Phys. 132 (1990) 245 (concept of event; see also Section VII.3 in the following book)
  • Local Quantum Physics: Fields, Particles, Algebras , Springer 1992, 2nd edition 1996. (Textbook)
  • with Detlev Buchholz: The quest for understanding relativistic quantum physics , Journal of Mathematical Physics 41 (2000) 3674–3697 (review and outlook)
  • Questions in quantum physics - a personal view , in: Fokas (Ed.): Mathematical Physics 2000 , Imperial College Press 2000. (Outlook)
  • Some people and some problems met in half a century of commitment to mathematical physics , The European Physics Journal H 35 (2010) 263–307 (personal memories)

literature

Web links

Footnotes

  1. ↑ Physikjournal 15 (2016) No. 4, 53 (obituary)
  2. ↑ Poggendorff Lit.-Biogr. Short dictionary Exact Wiss. , 1958
  3. ↑ Haag's theorem says that one can not use the usual Fock space representation to describe interacting relativistic quantum fields with canonical commutation relations ; one needs inequivalent Hilbert space representations of the fields; see also Encyclopedia of Mathematics
  4. ↑ See e.g. B. the review article Scattering in Relativistic Quantum Field Theory , arxiv : math-ph / 0509047
  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. ↑ An overview of the construction of a large number of models with these methods can be found in: Gandalf Lechner, Algebraic Constructive Quantum Field Theory: Integrable Models and Deformation Techniques , pp. 397–449 in: Advances in Algebraic Quantum Field Theory, Springer, 2015
  7. ↑ 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.
personal data
SURNAME Hague, Rudolf
BRIEF DESCRIPTION German theoretical physicist
DATE OF BIRTH 17th August 1922
PLACE OF BIRTH Tübingen
DATE OF DEATH 5th January 2016
Place of death Fischhausen-Neuhaus