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Adinkra Symbols (physics)
In 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 ... and Supersymmetry, supersymmetric representation theory, Adinkra symbols are a graphical representation of Supersymmetry algebra, supersymmetric algebras. Mathematically they can be described as colored finite connected simple graphs, that are bipartite graph, bipartite and regular graph, n-regular. Their name is derived from Adinkra symbols Adinkra symbols, of the same name, and they were introduced by Michael Faux and Sylvester James Gates in 2004. Overview One approach to the representation theory of super Lie algebras is to restrict attention to representations in one space-time dimension and having N supersymmetry generators, i.e., to (1, N) superalgebras. In that case, the defining algebraic relationship ... [...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 a superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes gravity arise in a natural way. Gravitons Like any field theory of gravity, a supergravity theory 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 Pran Nath in 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist. Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics. In supersymmetry, each particle from one class would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. For example, if the electron exists in a supersymmetric theory, then there would be a particle called a ''"selectron"'' (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly " unbroken" supersymmetry, each pair of superpartners would share the same mass and intern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representation Theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication). The theory of matrices and linear operators is well-understood, so representations of more abstract objects in terms of familiar linear algebra objects helps glean properties and sometimes simplify calculations on more abstract theories. The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these (and historically the first) is the representation theory of groups, in which elements of a group are represented by invertible matrices in such a way that the group operation i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry Algebra
In theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains not only the Poincaré algebra and a compact subalgebra of internal symmetries, but also contains some fermionic supercharges, transforming as a sum of ''N'' real spinor representations of the Poincaré group. Such symmetries are allowed by the Haag–Łopuszański–Sohnius theorem. When ''N''>1 the algebra is said to have extended supersymmetry. The supersymmetry algebra is a semidirect sum of a central extension of the super-Poincaré algebra by a compact Lie algebra ''B'' of internal symmetries. Bosonic fields commute while fermionic fields anticommute. In order to have a transformation that relates the two kinds of fields, the introduction of a Z2-grading under which the even elements are bosonic and the odd elements are fermionic is required. Such an algebra is called a Lie superalgebra. J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Graph
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called '' vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bipartite Graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V, that is every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the ''parts'' of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets U and V may be thought of as a coloring of the graph with two colors: if one colors all nodes in U blue, and all nodes in V red, each edge has endpoints of differing colors, as is required in the graph coloring problem.. In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle: after one node is colored blue and another red, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color. One often writes G=(U,V,E) to denote a bipartite graph whose partition has the parts U and V, with E denoting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Graph
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other. A regular graph with vertices of degree is called a graph or regular graph of degree . Also, from the handshaking lemma, a regular graph contains an even number of vertices with odd degree. Regular graphs of degree at most 2 are easy to classify: a graph consists of disconnected vertices, a graph consists of disconnected edges, and a graph consists of a disjoint union of cycles and infinite chains. A graph is known as a cubic graph. A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number of neighbors in common, and every non-adjacent pair of vertices has the same number of neighbors in common. The smallest graphs that are regular but not strong ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adinkra Symbols
''Adinkra'' are symbols from Ghana that represent concepts or aphorisms. ''Adinkra'' are used extensively in fabrics, logos and pottery. They are incorporated into walls and other architectural features. ''Adinkra'' symbols appear on some traditional Akan goldweights. The symbols are also carved on stools for domestic and ritual use. Tourism has led to new departures in the use of the symbols in items such as T-shirts and jewellery. The symbols have a decorative function but also represent objects that encapsulate evocative messages conveying traditional wisdom, aspects of life, or the environment. There are many symbols with distinct meanings, often linked with proverbs. In the words of Kwame Anthony Appiah, they were one of the means for "supporting the transmission of a complex and nuanced body of practice and belief". History Adinkra symbols were originally created by the Bono people of Gyaaman, Gyaman. The Gyaman king, List of rulers of the Akan state of Gyaaman, Nana ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylvester James Gates
Sylvester James Gates Jr. (born December 15, 1950), known as S. James Gates Jr. or Jim Gates, is an American theoretical physicist who works on supersymmetry, supergravity, and superstring theory. He currently holds the Clark Leadership Chair in Science with the physics department at the University of Maryland College of Computer, Mathematical, and Natural Sciences. He is also affiliated with the University Maryland's School of Public Policy. He served on former President Barack Obama's Council of Advisors on Science and Technology. Biography Gates, the oldest of four siblings, was born in Tampa, Florida, the son of Sylvester James Gates Sr. a career U.S. Army man, and Charlie Engels Gates. His mother died when he was 11. When his father remarried, his stepmother, a teacher, brought books into the home and emphasized the importance of education. The family moved many times while Gates was growing up, but, as he was entering 11th grade, settled in Orlando, Florida, where James att ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry Generator
In a supersymmetric theory 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. Supersymmetry is a Spacetime symmetries, spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued Spin (physics), spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics. In supersymmetry, each particle from one class would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. For example, if the electron exists in a supersymmetric theory, then there would be a particle called a ''"selectron"'' (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly "broken symmetry, unbroken" supersy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman Diagram
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to David Kaiser, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." While the diagrams are applied primarily to quantum field theory, they can also be used in other fields, such as solid-state theory. Frank Wilczek wrote that the calculations that won him the 2004 Nobel Prize in Physics "would have been literally unthinkable without Feynman diagra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
