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Green–Schwarz Mechanism
The Green–Schwarz mechanism (sometimes called the Green–Schwarz anomaly cancellation mechanism) is the main discovery that started the first superstring revolution in superstring theory. Discovery In 1984, Michael Green and John H. Schwarz realized that the anomaly in type I string theory with the gauge group SO(32) cancels because of an extra "classical" contribution from a 2-form field. They realized that one of the necessary conditions for a superstring theory to make sense is that the dimension of the gauge group of type I string theory must be 496 and then demonstrated this to be so. In the original calculation, gauge anomalies, mixed anomalies, and gravitational anomalies were expected to arise from a hexagon Feynman diagram. For the special choice of the gauge group SO(32) or E8 x E8, however, the anomaly factorizes and may be cancelled by a tree diagram. In string theory, this indeed occurs. The tree diagram describes the exchange of a virtual quantum of the B-fie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Superstring Revolution
The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum gravity, particle and condensed matter physics, cosmology, and pure mathematics. 1943–1959: S-matrix theory String theory represents an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 following John Archibald Wheeler's 1937 introduction of the S-matrix. Many prominent theorists picked up and advocated S-matrix theory, starting in the late 1950s and throughout the 1960s. The field became marginalized and discarded in the mid 1970s and disappeared in the 1980s. Physicists neglected it because some of its mathematical methods were alien, and because quantum chromodynamics supplanted it as an experimentally better-qualified approach to the strong interactions. The theory presented a radical rethinking ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hexagon
In geometry, a hexagon (from Ancient Greek, Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple polygon, simple (non-self-intersecting) hexagon is 720°. Regular hexagon A ''regular polygon, regular hexagon'' has Schläfli symbol and can also be constructed as a Truncation (geometry), truncated equilateral triangle, t, which alternates two types of edges. A regular hexagon is defined as a hexagon that is both equilateral polygon, equilateral and equiangular polygon, equiangular. It is bicentric polygon, bicentric, meaning that it is both cyclic polygon, cyclic (has a circumscribed circle) and tangential polygon, tangential (has an inscribed circle). The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals \tfrac times the apothem (radius of the inscribed figure, inscribed circle). All internal angles are 120 degree (angle), degrees. A regular hexago ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anomalies (physics)
Anomaly may refer to: Science Natural *Anomaly (natural sciences) **Atmospheric anomaly **Geophysical anomaly Medical *Congenital anomaly (birth defect), a disorder present at birth ** Physical anomaly, a deformation of an anatomical structure ***Congenital vertebral anomaly, any of several malformations of the spine **Collie eye anomaly, eye disease of dogs *** Coronary artery anomaly, a congenital abnormality in the heart ***Ebstein's anomaly, a congenital heart defect in which the opening of the tricuspid valve is displaced *** Uhl anomaly, a congenital heart disease affecting the myocardial muscle ***Vaginal anomalies Biology * Anomalous, a species of moth in the Noctuid family * Chromosome anomaly, a disorder caused by a structural error in a chromosome or an atypical number of chromosomes *Genetic anomaly, a disorder caused by mutation *Teratology, the study of developmental anomalies Physics *Anomalous diffusion is the movement of molecules from a region of lower conce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalb–Ramond Field
In theoretical physics in general and string theory in particular, the Kalb–Ramond field (named after Michael Kalb and Pierre Ramond), also known as the Kalb–Ramond ''B''-field or Kalb–Ramond NS–NS ''B''-field, is a quantum field that transforms as a two- form, i.e., an antisymmetric tensor field with two indices. The adjective "NS" reflects the fact that in the RNS formalism, these fields appear in the NS–NS sector in which all vector fermions are anti-periodic. Both uses of the word "NS" refer to André Neveu and John Henry Schwarz, who studied such boundary conditions (the so-called Neveu–Schwarz boundary conditions) and the fields that satisfy them in 1971. Details The Kalb–Ramond field generalizes the electromagnetic potential but it has two indices instead of one. This difference is related to the fact that the electromagnetic potential is integrated over one-dimensional worldlines of particles to obtain one of its contributions to the action while the Kalb†... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SUSY
Susy is a feminine given name, sometimes a short form (hypocorism) of Susan, Susanne, Susannah, etc. ''Susy'' may refer to: People * Susy Andersen (born 1940), Italian actress * Susanne Augustesen (b. 1956), Danish footballer * Susy Avery (born 1947), American politician * Olivia Susan Susy Clemens (1872-1896), a daughter of Mark Twain * Susy Delgado (born 1949), Paraguayan poet and writer * Isabella Susy De Martini (born 1952), Italian politician and academic * Susy Dorn, Peruvian teacher and musician born Susana Gabriela Rodriguez Santander in 1974 * Susy Frankel, New Zealand law academic * Susy Kane (born 1978), English actress and writer * Susannah Susy Pryde (born 1973), New Zealand cyclist * Susy Schultz, Chicago journalist and social advocate * Susy Thunder, hacker Susan Headley (born 1959) * Susi Wirz (b. 1931), Swiss figure skater Fictional characters * Susy Hendrix, blind character played by Audrey Hepburn in ''Wait Until Dark'' (film) See also * Susie (disambiguati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ricci Tensor
In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space. The Ricci tensor can be characterized by measurement of how a shape is deformed as one moves along geodesics in the space. In general relativity, which involves the pseudo-Riemannian setting, this is reflected by the presence of the Ricci tensor in the Raychaudhuri equation. Partly for this reason, the Einstein field equations propose that spacetime can be described by a pseudo-Riemannian metric, with a strikingly simple relationship between the Ricci tensor and the matter content of the universe. Like the metric tensor, the Ricci tensor assigns to each tangent space of the manifold a symmetric bili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Everything
A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the universe. Finding a theory of everything is one of the major unsolved problems in physics. String theory and M-theory have been proposed as theories of everything. Over the past few centuries, two theoretical frameworks have been developed that, together, most closely resemble a theory of everything. These two theories upon which all modern physics rests are general relativity and quantum mechanics. General relativity is a theoretical framework that only focuses on gravity for understanding the universe in regions of both large scale and high mass: planets, stars, galaxies, clusters of galaxies etc. On the other hand, quantum mechanics is a theoretical framework that only focuses on the three non-gravitational forces for under ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Elegant Universe
''The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory'' is a book by Brian Greene published in 1999, which introduces string and superstring theory, and provides a comprehensive though non-technical assessment of the theory and some of its shortcomings. In 2000, it won the Royal Society Prize for Science Books and was a finalist for the Pulitzer Prize for General Non-Fiction. A new edition was released in 2003, with an updated preface. Table of contents * Preface (with an additional preface to the 2003 edition) * Part I: The Edge of Knowledge * Part II: The Dilemma of Space, Time, and the Quanta * Part III: The Cosmic Symphony * Part IV: String Theory and the Fabric of Spacetime * Part V: Unification in the Twenty-First Century Contents Beginning with a brief consideration of classical physics, which concentrates on the major conflicts in physics, Greene establishes a historical context for string theory as a necessary means of integrati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, and conde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8. The designation E8 comes from the Cartan–Killing classification of the complex simple Lie algebras, which fall into four infinite series labeled A''n'', B''n'', C''n'', D''n'', and five exceptional cases labeled G2, F4, E6, E7, and E8. The E8 algebra is the largest and most complicated of these exceptional cases. Basic description The Lie group E8 has dimension 248. Its rank, which is the dimension of its maximal torus, is eight. Therefore, the vectors of the root system are in eight-dimensional Euclidean space: they are described explicitly later in this article. The Weyl group of E8, which is the group of symmetries of the maximal torus which are induced by conjugations in the whole group, has order 2357 = . The compact group E8 is unique ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
