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]
Biography
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]
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
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]
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, Rudolf; Lopuszanski, Jan T.; Sohnius, Martin (1975). "All possible generators of supersymmetries of the S-matrix". Nuclear Physics B. 88 (2): 257–274.
Bibcode:
1975NuPhB..88..257H.
doi:
10.1016/0550-3213(75)90279-5. (Classification of Supersymmetry.)
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.
ISBN978-3-662-46422-9.
^Since the laboratory in
Geneva was still under construction, the study group was hosted by the
Niels Bohr Institute in Copenhagen.[6]
^Käthe Fues was one of the daughters of the German theoretical physicist
Erwin Fues.[14]
^Haag married Barbara Klie after Käthe's premature death.
^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]
^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.
^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]
^An overview of the construction of a large number of models using these methods can be found in Lechner's chapter.[25]
^He was critical of
string theory, arguing a misunderstanding of the concept of particle in the conventional framework of quantum field theory.[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.
^Haag, Rudolf; Haag, Anna (2003). Leben und gelebt werden: Erinnerungen und Betrachtungen (in German) (1 ed.). Silberburg.
ISBN978-3874075626. 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.
ISBN978-3034318181.
^Poggendorff, Johann C. (1958). J.C. Poggendorffs biographisch-literarisches Handwörterbuch zur Geschichte der exacten Wissenschaften (in German). J.A. Barth.
^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.
S2CID188592087.
^"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.
ISBN978-3-540-26832-1.
^Buchholz, Detlev; Doplicher, Sergio; Fredenhagen, Klaus (2016).
"Rudolf Haag (1922 - 2016)"(PDF). News Bulletin, International Association of Mathematical Physics: 27–31.
^"Haag theorem". Encyclopedia of Mathematics. Retrieved 9 January 2021.
^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.
ISBN978-3-319-21352-1.
Buchholz, Detlev; Doplicher, Sergio; Fredenhagen, Klaus (2016).
"Rudolf Haag (1922 - 2016)"(PDF). News Bulletin, International Association of Mathematical Physics: 27–31.
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.
S2CID188592087.
Buchholz, Detlev; Fredenhagen, Klaus (2016).
"Nachruf auf Rudolf Haag". Physik Journal (in German). 15 (4): 53.