Robert Schrader
   HOME

TheInfoList



OR:

Robert Schrader (12 September 1939 – 29 November 2015)text of obituary at math.uni-bonn.de
/ref> was a German theoretical and mathematical physicist and professor of the
Free University of Berlin The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public university, public research university in Berlin, Germany. It was founded in West Berlin in 1948 with American support during the early Cold War period a ...
. He is known for the
Osterwalder–Schrader axioms In quantum field theory, the Wightman distributions can be analytically continued to analytic functions in Euclidean space with the domain restricted to ordered ''n''-tuples in \mathbb R^d that are pairwise distinct. These functions are called ...
.


Biography

Robert Schrader was born in Berlin, Germany in 1939. From 1959 to 1964 Schrader studied physics at
Kiel University Kiel University, officially the Christian Albrecht University of Kiel, (, abbreviated CAU, known informally as Christiana Albertina) is a public University, public research university in the city of Kiel, Germany. It was founded in 1665 as the ...
, the
University of Zurich The University of Zurich (UZH, ) is a public university, public research university in Zurich, Switzerland. It is the largest university in Switzerland, with its 28,000 enrolled students. It was founded in 1833 from the existing colleges of the ...
, and the
University of Hamburg The University of Hamburg (, also referred to as UHH) is a public university, public research university in Hamburg, Germany. It was founded on 28 March 1919 by combining the previous General Lecture System ('':de:Allgemeines Vorlesungswesen, ...
, where he completed his
Diplom A ''Diplom'' (, from ) is an academic degree in the German-speaking countries Germany, Austria, and Switzerland and a similarly named degree in some other European countries including Albania, Bulgaria, Belarus, Bosnia and Herzegovina, Croatia ...
in 1964. His Diplom thesis ''Die Charaktere der inhomogenen Lorentzgruppe'' (The characters of the inhomogeneous
Lorentz group In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physi ...
) was supervised by
Harry Lehmann Harry Lehmann (21 March 1924 in Güstrow22 November 1998 in Hamburg) was a German physicist. Known for his work on correlation functions in quantum field theory. Biography Lehmann studied physics at Rostock and the Humboldt-Universität zu Berl ...
and Hans Joos. In 1965 he went to
ETH Zurich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ran ...
, where he worked as an assistant and received his doctorate ( ''Promotion'') in 1969 under the supervision of
Klaus Hepp Klaus Hepp (born 11 December 1936) is a German-born Swiss theoretical physicist working mainly in quantum field theory. Hepp studied mathematics and physics at Westfälischen Wilhelms-Universität in Münster and at the Eidgenössischen Technis ...
and
Res Jost Res Jost (10 January 1918 – 3 October 1990) was a Swiss theoretical physicist, who worked mainly in constructive quantum field theory. Biography Res Jost was born on January 10, 1918, in Bern. He is the son of the physics teacher Wilhelm ...
. His thesis, published in ''
Communications in Mathematical Physics ''Communications in Mathematical Physics'' is a peer-reviewed academic journal published by Springer. The journal publishes papers in all fields of mathematical physics, but focuses particularly in analysis related to condensed matter physics, sta ...
'', dealt with the Lee model introduced in 1954 by
Tsung-Dao Lee Tsung-Dao Lee (; November 24, 1926 – August 4, 2024) was a Chinese-American physicist, known for his work on parity violation, the Lee–Yang theorem, particle physics, relativistic heavy ion (RHIC) physics, nontopological solitons, and ...
. From 1970 to 1973 Schrader was a research fellow at
Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...
and at
Princeton University Princeton University is a private university, private Ivy League research university in Princeton, New Jersey, United States. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial ...
. At Harvard under the supervision of
Arthur Jaffe Arthur Michael Jaffe (; born December 22, 1937) is an American mathematical physicist at Harvard University, where in 1985 he succeeded George Mackey as the Landon T. Clay Professor of Mathematics and Theoretical Science. Education and career ...
, he worked with
Konrad Osterwalder Konrad Osterwalder (born June 3, 1942) is a Swiss mathematician and physicist, former Undersecretary-General of the United Nations, former Rector of the United Nations University (UNU), and Rector Emeritus of the Swiss Federal Institute of Techno ...
on Euclidean quantum field theory. In 1971 Schrader
habilitated Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excellen ...
at the University of Hamburg with the thesis ''Das Yukawa Modell in zwei Raum-Zeit-Dimensionen'' (The Yukawa model in two space-time dimensions). He was a professor of theoretical physics at the
Free University of Berlin The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public university, public research university in Berlin, Germany. It was founded in West Berlin in 1948 with American support during the early Cold War period a ...
from 1973 until his retirement in 2005. He was a visiting scientist in 1974 and again in 1980 at the IHÉS at
Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...
, in 1976 in Harvard, in 1979 at
CERN The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in Meyrin, western suburb of Gene ...
, for the academic year 1986/87 at the
Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...
, and in 1989 at the ETH. For two academic years from 1982 to 1984, he was a visiting professor at the
State University of New York at Stony Brook Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public university, public research university in Stony Brook, New York, United States, on Long Island. Along with the University at Buffalo, it is on ...
. Schrader was the author or coauthor of more than 100 scientific publications. He dealt with
axiomatic quantum field theory Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years ...
and, with Konrad Osterwalder, introduced in 1973 the Osterwalder–Schrader axioms for Euclidean
Green's function In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if L is a linear dif ...
s. Arthur Jaffe suggested to his postdocs Osterwalder and Schrader that they study the work on the Euclidean formulation of
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...
(QFT) done by Kurt Symanzik and
Edward Nelson Edward Nelson (May 4, 1932 – September 10, 2014) was an American mathematician. He was professor in the Mathematics Department at Princeton University. He was known for his work on mathematical physics and mathematical logic. In mathematical l ...
. The two postdocs published a set of axioms, which contained the crucial property called reflection positivity (RP), also referred to as Osterwalder–Schrader positivity. The Osterwalder–Schrader reconstruction theorem states that the Wightman functions of a relativistic QFT can be reconstructed from the
Schwinger function In quantum field theory, the Wightman distributions can be analytically continued to analytic functions in Euclidean space with the domain restricted to ordered ''n''-tuples in \mathbb R^d that are pairwise distinct. These functions are called ...
s of a Euclidean theory satisfying the Osterwalder-Schrader axioms. RP is important for
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applicati ...
and
lattice gauge theory In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important in particle physics, and include the prevailing theories of elementary particles: quantum ele ...
. Schrader worked on many other areas of mathematical and theoretical physics, such as
Yang–Mills theory Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special un ...
, invariants of three-dimensional manifolds, lattice formulation of gravitational theory,
quantum chaos Quantum chaos is a branch of physics focused on how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that quantum chaos seeks to answer is: "What is the relationship between quantum mechanics ...
, and possibilities for measuring gravitational waves with
SQUID A squid (: squid) is a mollusc with an elongated soft body, large eyes, eight cephalopod limb, arms, and two tentacles in the orders Myopsida, Oegopsida, and Bathyteuthida (though many other molluscs within the broader Neocoleoidea are also ...
s. His extensive collaboration with Vadim Korstrykin included research on
quantum wire In mesoscopic physics, a quantum wire is an electrically conducting wire in which quantum effects influence the transport properties. Usually such effects appear in the dimension of nanometers, so they are also referred to as nanowires. Quantum ...
s and Laplacian operators on metric graphs. He died from cancer in 2015.


Selected publications

* * * * * * * * * *


References


External links

* (with extensive publication list)
''Robert Schrader'' (brief bio)
archived from Ray Streater's home page at King's College London * {{DEFAULTSORT:Schrader, Robert 1939 births 2015 deaths 20th-century German physicists 21st-century German physicists Mathematical physicists German theoretical physicists University of Hamburg alumni ETH Zurich alumni Academic staff of the Free University of Berlin People associated with CERN