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Supermathematics
Supermathematics is the branch of mathematical physics which applies the mathematics of Lie superalgebras to the behaviour of bosons and fermions. The driving force in its formation in the 1960s and 1970s was Felix Berezin. Objects of study include superalgebras (such as super Minkowski space and super-Poincaré algebra), superschemes, supermetrics/supersymmetry, supermanifolds, supergeometry, and supergravity, namely in the context of superstring theory. References "The importance of Lie algebras" Professor Isaiah Kantor, Lund University External links * Felix Berezin, The Life and Death of the Mastermind of Supermathematics', edited by Mikhail Shifman Mikhail "Misha" Arkadyevich Shifman (; born 4 April 1949) is a theoretical physicist (high energy physics), formerly at the Institute for Theoretical and Experimental Physics, Moscow, Ida Cohen Fine Professor of Theoretical Physics, William I. ..., World Scientific, Singapore, 2007, Mathematical physics Supersymmetry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supermanifold
In physics and mathematics, supermanifolds are generalizations of the manifold concept based on ideas coming from supersymmetry. Several definitions are in use, some of which are described below. Informal definition An informal definition is commonly used in physics textbooks and introductory lectures. It defines a supermanifold as a manifold with both bosonic and fermionic coordinates. Locally, it is composed of coordinate charts that make it look like a "flat", "Euclidean" superspace. These local coordinates are often denoted by :(x,\theta,\bar) where ''x'' is the ( real-number-valued) spacetime coordinate, and \theta\, and \bar are Grassmann-valued spatial "directions". The physical interpretation of the Grassmann-valued coordinates are the subject of debate; explicit experimental searches for supersymmetry have not yielded any positive results. However, the use of Grassmann variables allow for the tremendous simplification of a number of important mathematical results. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics is the development of mathematics, 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, known as physical mathematics. Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. Classical mechanics Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints). Both formulations are embodied in analytical mechanics and lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry
Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It proposes that for every known particle, there exists a partner particle with different spin properties. There have been multiple experiments on supersymmetry that have failed to provide evidence that it exists in nature. If evidence is found, supersymmetry could help explain certain phenomena, such as the nature of dark matter and the hierarchy problem in particle physics. A supersymmetric theory is a theory in which the equations for force and the equations for matter are identical. In theoretical physics, theoretical and mathematical physics, any theory with this property has the ''principle of supersymmetry'' (SUSY). Dozens of supersymmetric theories exist. In theory, supersymmetry is a type of Spacetime symmetries, spacetime symmetry betwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Physics
Mathematical physics is the development of mathematics, 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, known as physical mathematics. Scope There are several distinct branches of mathematical physics, and these roughly correspond to particular historical parts of our world. Classical mechanics Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints). Both formulations are embodied in analytical mechanics and lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mikhail Shifman
Mikhail "Misha" Arkadyevich Shifman (; born 4 April 1949) is a theoretical physicist (high energy physics), formerly at the Institute for Theoretical and Experimental Physics, Moscow, Ida Cohen Fine Professor of Theoretical Physics, William I. Fine Theoretical Physics Institute, University of Minnesota. Scientific contributions Shifman is known for a number of basic contributions to quantum chromodynamics, the theory of strong interactions, and to understanding of supersymmetric gauge dynamics. The most important results due to M. Shifman are diverse and include (i) the discovery of the penguin mechanism in the flavor-changing weak decays (1974); (ii) introduction of the gluon condensate and development of the SVZ sum rules relating properties of the low-lying hadronic states to the vacuum condensates (1979); (iii) introduction of the invisible (aka KSVZ) axion (1980) (iv) first exact results in supersymmetric Yang–Mills theories (NSVZ beta function, gluino condensate,198 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lund University
Lund University () is a Public university, public research university in Sweden and one of Northern Europe's oldest universities. The university is located in the city of Lund in the Swedish province of Scania. The university was officially founded in 1666 on the location of the old ''studium generale'' next to Lund Cathedral. Lund University has nine Faculty (division), faculties, with additional campuses in the cities of Malmö and Helsingborg, with around 47,000 students in 241 different programmes and 1,450 freestanding courses. The university has 560 partner universities in approximately 70 countries. It belongs to the League of European Research Universities as well as the global Universitas 21 network. Among those associated with the university are five Nobel Prize winners, a Fields Medal winner, prime ministers and business leaders. Two major facilities for materials research have been recent strategic priorities in Lund: MAX IV, a synchrotron radiation laboratory – in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isaiah Kantor
Isaiah Kantor (or Issai Kantor, or Isai Lʹvovich Kantor) (1936–2006) was a mathematician who introduced the Kantor–Koecher–Tits construction, and the Kantor double, a Jordan superalgebra constructed from a Poisson algebra In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also a derivation. Poisson algebras appear naturally in Hamiltonian mechanics, and are also central .... References * Russian mathematicians 2006 deaths 1936 births {{Russia-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superstring Theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions and bosons and incorporates supersymmetry to model gravity. Since the second superstring revolution, the five superstring theories ( Type I, Type IIA, Type IIB, HO and HE) are regarded as different limits of a single theory tentatively called M-theory. Background One of the deepest open problems in theoretical physics is formulating a theory of quantum gravity. Such a theory incorporates both the theory of general relativity, which describes gravitation and applies to large-scale structures, and quantum mechanics or more specifically quantum field theory, which describes the other three fundamental forces that act on th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local supersymmetry. Since the supersymmetry (SUSY) generators form together with the Poincaré algebra and superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes gravity arise in a natural way. Gravitons Like all covariant approaches to quantum gravity, supergravity contains a spin-2 field whose quantum is the graviton. Supersymmetry requires the graviton field to have a superpartner. This field has spin 3/2 and its quantum is the gravitino. The number of gravitino fields is equal to the number of supersymmetries. History Gauge supersymmetry The first theory of local supersymmetry was proposed by Dick Arnowitt and Pra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supergeometry
Supergeometry is differential geometry of modules over graded commutative algebras, supermanifolds and graded manifolds. Supergeometry is part and parcel of many classical and quantum field theories involving odd fields, e.g., SUSY field theory, BRST theory, or supergravity. Supergeometry is formulated in terms of \mathbb Z_2-graded modules and sheaves over \mathbb Z_2-graded commutative algebras ( supercommutative algebras). In particular, superconnections are defined as Koszul connections on these modules and sheaves. However, supergeometry is not particular noncommutative geometry because of a different definition of a graded derivation. Graded manifolds and supermanifolds also are phrased in terms of sheaves of graded commutative algebras. Graded manifolds are characterized by sheaves on smooth manifolds, while supermanifolds are constructed by gluing of sheaves of supervector spaces. There are different types of supermanifolds. These are smooth supermanifolds ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry
Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It proposes that for every known particle, there exists a partner particle with different spin properties. There have been multiple experiments on supersymmetry that have failed to provide evidence that it exists in nature. If evidence is found, supersymmetry could help explain certain phenomena, such as the nature of dark matter and the hierarchy problem in particle physics. A supersymmetric theory is a theory in which the equations for force and the equations for matter are identical. In theoretical physics, theoretical and mathematical physics, any theory with this property has the ''principle of supersymmetry'' (SUSY). Dozens of supersymmetric theories exist. In theory, supersymmetry is a type of Spacetime symmetries, spacetime symmetry betwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Superalgebra
In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a \Z/2\Z grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry. The notion of \Z/2\Z grading used here is distinct from a second \Z/2\Z grading having cohomological origins. A graded Lie algebra (say, graded by \Z or \N) that is anticommutative and has a graded Jacobi identity also has a \Z/2\Z grading; this is the "rolling up" of the algebra into odd and even parts. This rolling-up is not normally referred to as "super". Thus, supergraded Lie superalgebras carry a ''pair'' of \Z/2\Zgradations: one of which is supersymmetric, and the other is classical. Pierre Deligne calls the supersymmetric one the ''super gradation'', and the classical one the ''cohomological gradation''. These two gradations must be compatible, and there is often disagreement as to how they should be regarded. Definition Formally, a Lie superalgebra is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
