1. Introduction

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.^[1]

2. Biography

Rudolf Haag was born on August 17, 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.^[2] 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 labor to study physics and mathematics as an autodidact.^[3]

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^[4] and became his assistant until 1956. In April 1953, he joined the CERN theoretical study group in Copenhagen^[5] directed by Niels Bohr.^[6][7] After a year, he returned to his assistant position in Munich and completed the German habilitation in 1954.^[8] From 1956 to 1957 he worked with Werner Heisenberg at the Max Planck Institute for Physics in Göttingen.^[9]

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 in 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.^[10] In 1966, he accepted the professorship position for theoretical physics at the University of Hamburg, where he stayed until he retired in 1987.^[11] After retirement, he worked on the concept of quantum physical event.^[12]

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,^[13] with whom he had four children, Albert, Friedrich, Elisabeth, and Ulrich. After retirement, he moved together with his second wife Barbara Klie^[14] to Schliersee, a pastoral village in the Bavarian mountains. He died on January 5, 2016, in Fischhausen-Neuhaus, in southern Bavaria.^[15]

3. Scientific Career

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.^[16] 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.^[20] 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.^[21][22] These results were later generalized for arbitrary sectors in the Doplicher–Roberts duality theorem.^[23] 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.^[24]

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 (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^[25] also in the construction of concrete quantum field theoretical models.^[26] Together with Daniel Kastler and Ewa Trych-Pohlmeyer, Haag also succeeded in deriving the KMS condition from the stability properties of thermal equilibrium states.^[27] Together with Huzihiro Araki, Daniel Kastler, and Masamichi Takesaki, he also developed a theory of chemical potential in this context.^[28]

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.^[29]

Haag had a certain mistrust towards what he viewed as speculative developments in theoretical physics^[6] 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.^[30][31]

4. Honors and Awards

In 1970 Haag received the Max Planck Medal for outstanding achievements in theoretical physics^[32] and in 1997 the Henri Poincaré Prize^[33] for his fundamental contributions to quantum field theory as one of the founders of the modern formulation.^[1] Since 1980 Haag was a member of the German National Academy of Sciences Leopoldina^[34] and since 1981 of the Göttingen Academy of Sciences.^[35] Since 1979 he was a corresponding member of the Bavarian Academy of Sciences^[36] and since 1987 of the Austrian Academy of Sciences.^[37]

5. Publications

5.1. Textbook

• 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. 

5.2. Selected Scientific Works

• Haag, Rudolf (1955). "On quantum field theories". Dan. Mat. Fys. Medd. 29 (12): 1–37. http://cds.cern.ch/record/212242.  (Haag's theorem.)

• Haag, Rudolf (1958). "Quantum field theories with composite particles and asymptotic conditions". Physical Review 112 (2): 669–673. doi:10.1103/PhysRev.112.669. Bibcode: 1958PhRv..112..669H.  (Haag–Ruelle scattering theory.)

• Haag, Rudolf; Kastler, Daniel (1964). "An Algebraic approach to quantum field theory". Journal of Mathematical Physics 5 (7): 848–861. doi:10.1063/1.1704187. Bibcode: 1964JMP.....5..848H.  (Haag–Kastler axioms.)

• Doplicher, Sergio; Haag, Rudolf; Roberts, John E. (1971). "Local observables and particle statistics. 1". Communications in Mathematical Physics 23 (3): 199–230. doi:10.1007/BF01877742. Bibcode: 1971CMaPh..23..199D. https://projecteuclid.org/euclid.cmp/1103857630. 

• Doplicher, Sergio; Haag, Rudolf; Roberts, John E. (1974). "Local observables and particle statistics. 2". Communications in Mathematical Physics 35 (1): 49–85. doi:10.1007/BF01646454. Bibcode: 1974CMaPh..35...49D. https://projecteuclid.org/euclid.cmp/1103859518.  (Doplicher-Haag-Roberts analysis of the superselection structure.)

• Haag, Rudolf; Hugenholtz, Nico M.; Winnink, Marius (1967). "On the Equilibrium states in quantum statistical mechanics". Communications in Mathematical Physics 5 (3): 215–236. doi:10.1007/BF01646342. Bibcode: 1967CMaPh...5..215H. https://projecteuclid.org/euclid.cmp/1103840050.  (KMS condition.)

• Haag, Rudolf; Kastler, Daniel; Trych-Pohlmeyer, Ewa B. (1974). "Stability and equilibrium states". Communications in Mathematical Physics 38 (3): 173–193. doi:10.1007/BF01651541. Bibcode: 1974CMaPh..38..173H. https://projecteuclid.org/euclid.cmp/1103860047.  (Stability and KMS condition.)

• Araki, Huzihiro; Kastler, Daniel; Takesaki, Masamichi; Haag, Rudolf (1977). "Extension of KMS States and Chemical Potential". Communications in Mathematical Physics 53 (2): 97–134. doi:10.1007/BF01609126. Bibcode: 1977CMaPh..53...97A. https://projecteuclid.org/euclid.cmp/1103900637.  (KMS condition and chemical potential.)

• Haag, Rudolf; Narnhofer, Heide; Stein, Ulrich (1984). "On Quantum Field Theory in Gravitational Background". Communications in Mathematical Physics 94 (2): 219–238. doi:10.1007/BF01209302. Bibcode: 1984CMaPh..94..219H. https://projecteuclid.org/euclid.cmp/1103941282.  (Unruh effect.)

• Fredenhagen, Klaus; Haag, Rudolf (1990). "On the Derivation of Hawking Radiation Associated With the Formation of a Black Hole". Communications in Mathematical Physics 127 (2): 273–284. doi:10.1007/BF02096757. Bibcode: 1990CMaPh.127..273F. https://projecteuclid.org/euclid.cmp/1104180137.  (Hawking radiation.)

• Haag, Rudolf; Lopuszanski, Jan T.; Sohnius, Martin (1975). "All possible generators of supersymmetries of the S-matrix". Nuclear Physics B 88 (2): 257–274. doi:10.1016/0550-3213(75)90279-5. Bibcode: 1975NuPhB..88..257H.  (Classification of Supersymmetry.)
• Haag, Rudolf (1990). "Fundamental Irreversibility and the Concept of Events". Communications in Mathematical Physics 132 (1): 245–252. doi:10.1007/BF02278010. Bibcode: 1990CMaPh.132..245H. https://projecteuclid.org/euclid.cmp/1104201040.  (Concept of Event.)

5.3. Others

• Buchholz, Detlev; Haag, Rudolf (2000). "The Quest for understanding in relativistic quantum physics". Journal of Mathematical Physics 41 (6): 3674–3697. doi:10.1063/1.533324. Bibcode: 2000JMP....41.3674B. 

• Haag, Rudolf (2000). "Questions in quantum physics: A Personal view". Mathematical Physics 2000: 87–100. doi:10.1142/9781848160224_0005. ISBN 978-1-86094-230-3. Bibcode: 2000hep.th....1006H. 

• 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. doi:10.1140/epjh/e2010-10032-4. Bibcode: 2010EPJH...35..263H. 

• 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 (3): 255–261. doi:10.1140/epjh/e2010-10042-7. Bibcode: 2010EPJH...35..255H. 

• Haag, Rudolf (2015). "Faces of Quantum Physics". The Message of Quantum Science. Lecture Notes in Physics. 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. doi:10.1142/S0219749919500370. Bibcode: 2019IJQI...1750037H.