In theoretical physics,quantum field theory (QFT) is a theoretical framework that combines classical field theory,special relativity,and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles.
The Standard Model of particle physics is the theory describing three of the four known fundamental forces in the universe and classifying all known elementary particles. It was developed in stages throughout the latter half of the 20th century,through the work of many scientists worldwide,with the current formulation being finalized in the mid-1970s upon experimental confirmation of the existence of quarks. Since then,proof of the top quark (1995),the tau neutrino (2000),and the Higgs boson (2012) have added further credence to the Standard Model. In addition,the Standard Model has predicted various properties of weak neutral currents and the W and Z bosons with great accuracy.
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,the Wightman axioms,named after Arthur Wightman,are an attempt at a mathematically rigorous formulation of quantum field theory. Arthur Wightman formulated the axioms in the early 1950s,but they were first published only in 1964 after Haag–Ruelle scattering theory affirmed their significance.
In quantum mechanics,the spin–statistics theorem relates the intrinsic spin of a particle to the particle statistics it obeys. In units of the reduced Planck constant ħ,all particles that move in 3 dimensions have either integer spin or half-integer spin.
Hilbert's sixth problem is to axiomatize those branches of physics in which mathematics is prevalent. It occurs on the widely cited list of Hilbert's problems in mathematics that he presented in the year 1900. In its common English translation,the explicit statement reads:
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.
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.
Barry Martin Simon is an American mathematical physicist and was the IBM professor of Mathematics and Theoretical Physics at Caltech,known for his prolific contributions in spectral theory,functional analysis,and nonrelativistic quantum mechanics,including the connections to atomic and molecular physics. He has authored more than 400 publications on mathematics and physics.
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.
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.
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.
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
