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 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 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. Haag had a certain mistrust towards what he viewed as speculative developments in theoretical physics 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. Honors and awards In 1970 Haag received the Max Planck Medal for outstanding achievements in theoretical physics and in 1997 the Henri Poincaré Prize for his fundamental contributions to quantum field theory as one of the founders of the modern formulation. Since 1980 Haag was a member of the German National Academy of Sciences Leopoldina and since 1981 of the Göttingen Academy of Sciences. Since 1979 he was a corresponding member of the Bavarian Academy of Sciences and since 1987 of the Austrian Academy of Sciences. Publications Textbook Selected scientific works (Haag's theorem.) (Haag–Ruelle scattering theory.) (Haag–Kastler axioms.) (Doplicher-Haag-Roberts analysis of the superselection structure.) (KMS condition.) (Stability and KMS condition.) (KMS condition and chemical potential.) (Unruh effect.) (Hawking radiation.) (Classification of Supersymmetry.) (Concept of Event.) Others See also Axiomatic quantum field theory Communications in Mathematical Physics Constructive quantum field theory Haag–Łopuszański–Sohnius theorem Haag–Ruelle scattering theory Haag's theorem Hilbert's sixth problem Local quantum physics Principle of locality Quantum field theory Quantum field theory in curved spacetime Notes References Further reading (With photo). (With photo). External links . . . . 20th-century German physicists 21st-century German physicists Academic staff of the University of Hamburg Winners of the Max Planck Medal Members of the Austrian Academy of Sciences Members