Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics.
Arthur Strong Wightman was an American mathematical physicist. He was one of the founders of the axiomatic approach to quantum field theory, and originated the set of Wightman axioms. With his rigorous treatment of quantum field theories, he promoted research on various aspects of modern mathematical physics.
Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework for quantum field theory, because it was introduced by Rudolf Haag and Daniel Kastler (1964). The axioms are stated in terms of an algebra given for every open set in Minkowski space, and mappings between those.
Jean-Marie Souriau was a French mathematician. He was one of the pioneers of modern symplectic geometry.
In mathematical physics, constructive quantum field theory is the field devoted to showing that quantum field theory can be defined in terms of precise mathematical structures. This demonstration requires new mathematics, in a sense analogous to classical real analysis, putting calculus on a mathematically rigorous foundation. Weak, strong, and electromagnetic forces of nature are believed to have their natural description in terms of quantum fields.
Rudolf Haag 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.
David Pierre Ruelle is a Belgian mathematical physicist, naturalized French. He has worked on statistical physics and dynamical systems. With Floris Takens, Ruelle coined the term strange attractor, and developed a new theory of turbulence.
Detlev Buchholz is a German theoretical physicist. He investigates quantum field theory, especially in the axiomatic framework of algebraic quantum field theory.
Daniel Kastler was a French theoretical physicist, working on the foundations of quantum field theory and on non-commutative geometry.
Arthur Michael Jaffe 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.
James Gilbert Glimm is an American mathematician, former president of the American Mathematical Society, and distinguished professor at Stony Brook University. He has made many contributions in the areas of pure and applied mathematics.
Konrad Osterwalder 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 Technology Zurich. He is known for the Osterwalder–Schrader theorem.
The Annals of Statistics is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics. It was started in 1973 as a continuation in part of the Annals of Mathematical Statistics (1930), which was split into the Annals of Statistics and the Annals of Probability.
Res Jost was a Swiss theoretical physicist, who worked mainly in constructive quantum field theory.
Jürg Martin Fröhlich is a Swiss mathematician and theoretical physicist. He is best known for introducing rigorous techniques for the analysis of statistical mechanics models, in particular continuous symmetry breaking, and for pioneering the study of topological phases of matter using low-energy effective field theories.
Huzihiro Araki was a Japanese mathematical physicist and mathematician who worked on the foundations of quantum field theory, on quantum statistical mechanics, and on the theory of operator algebras.
Ezra Getzler is an Australian mathematician and mathematical physicist.
Emilio Elizalde is a Spanish physicist working in the fields of gravitational physics and general relativity.
Sergio Doplicher is an Italian mathematical physicist, who mainly dealt with the mathematical foundations of quantum field theory and quantum gravity.
Klaus Fredenhagen is a German theoretical physicist who works on the mathematical foundations of quantum field theory.
