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.
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.
Ernst Carl Gerlach Stueckelberg was a Swiss mathematician and physicist,regarded as one of the most eminent physicists of the 20th century.
In quantum field theory,the Wightman distributions can be analytically continued to analytic functions in Euclidean space with the domain restricted to the ordered set of points in Euclidean space with no coinciding points. These functions are called the Schwinger functions and they are real-analytic,symmetric under the permutation of arguments,Euclidean covariant and satisfy a property known as reflection positivity. Properties of Schwinger functions are known as Osterwalder–Schrader axioms. Schwinger functions are also referred to as Euclidean correlation functions.
The Yang–Mills existence and mass gap problem is an unsolved problem in mathematical physics and mathematics,and one of the seven Millennium Prize Problems defined by the Clay Mathematics Institute,which has offered a prize of US$1,000,000 for its solution.
The Thirring model is an exactly solvable quantum field theory which describes the self-interactions of a Dirac field in (1+1) dimensions.
In theoretical physics,statistical field theory (SFT) is a theoretical framework that describes phase transitions. It does not denote a single theory but encompasses many models,including for magnetism,superconductivity,superfluidity,topological phase transition,wetting as well as non-equilibrium phase transitions. A SFT is any model in statistical mechanics where the degrees of freedom comprise a field or fields. In other words,the microstates of the system are expressed through field configurations. It is closely related to quantum field theory,which describes the quantum mechanics of fields,and shares with it many techniques,such as the path integral formulation and renormalization. If the system involves polymers,it is also known as polymer field theory.
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.
Valentine "Valya" Bargmann was a German-American mathematician and theoretical physicist.
In noncommutative geometry,the Jaffe- Lesniewski-Osterwalder (JLO) cocycle is a cocycle in an entire cyclic cohomology group. It is a non-commutative version of the classic Chern character of the conventional differential geometry. In noncommutative geometry,the concept of a manifold is replaced by a noncommutative algebra of "functions" on the putative noncommutative space. The cyclic cohomology of the algebra contains the information about the topology of that noncommutative space,very much as the de Rham cohomology contains the information about the topology of a conventional manifold.
Markus Eduard Fierz was a Swiss physicist,particularly remembered for his formulation of spin–statistics theorem,and for his contributions to the development of quantum theory,particle physics,and statistical mechanics. He was awarded the Max Planck Medal in 1979 and the Albert Einstein Medal in 1989 for all his work.
Res Jost was a Swiss theoretical physicist,who worked mainly in constructive quantum field theory.
Klaus Hepp 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 Technischen Hochschule (ETH) in Zurich,where,in 1962,with Res Jost as thesis first advisor and Markus Fierz as thesis second advisor,he received a doctorate for the thesis and at ETH in 1963 attained the rank of Privatdozent. From 1966 until his retirement in 2002 he was professor of theoretical physics there. From 1964 to 1966 he was at the Institute for Advanced Study in Princeton. Hepp was also Loeb Lecturer at Harvard and was at the IHÉS near Paris.
The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute has pledged a US$1 million prize for the first correct solution to each problem.
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.
Thomas C. Spencer is an American mathematical physicist,known in particular for important contributions to constructive quantum field theory,statistical mechanics,and spectral theory of random operators. He is an emeritus faculty member at the Institute for Advanced Study.
Joel Shalom Feldman is a Canadian mathematical physicist and mathematician.
Felix Finster is a German mathematician working on problems in mathematical physics,geometry and analysis.
Giovanni Felder is a Swiss mathematical physicist and mathematician,working at ETH Zurich. He specializes in algebraic and geometric properties of integrable models of statistical mechanics and quantum field theory.
Robert Schrader was a German theoretical and mathematical physicist. He is known for the Osterwalder–Schrader axioms.
Rector Osterwalder chairing UNU event on the work of the UN SC 1540 committee
UNU Rector Osterwalder with UNHCR Commissioner Gutteres at Rio+20 Press Conference
