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String Field Theory
String field theory (SFT) is a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory. This is accomplished at the level of perturbation theory by finding a collection of vertices for joining and splitting strings, as well as string propagators, that give a Feynman diagram-like expansion for string scattering amplitudes. In most string field theories, this expansion is encoded by a classical action found by second-quantizing the free string and adding interaction terms. As is usually the case in second quantization, a classical field configuration of the second-quantized theory is given by a wave function in the original theory. In the case of string field theory, this implies that a classical configuration, usually called the string field, is given by an element of the free string Fock space. The principal advantages of the formalism are that it allows the computation of off-shell amplitudes and, ... [...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 acts like a 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 condensed matter ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Transformation
In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths. More formally, let U and V be open subsets of \mathbb^n. A function f:U\to V is called conformal (or angle-preserving) at a point u_0\in U if it preserves angles between directed curves through u_0, as well as preserving orientation. Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size or curvature. The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. The transformation is conformal whenever the Jacobian at each point is a positive scalar times a rotation matrix (orthogonal with determinant one). Some authors define conformality to include orientation-reversing mappings whose Jacobians can be written as any scalar times any orthogonal matrix. For mappings in two dimensions, the (orientation-preserving) conformal mappings are precisely the locall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Killing Vector Field
In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a pseudo-Riemannian manifold that preserves the metric tensor. Killing vector fields are the infinitesimal generators of isometries; that is, flows generated by Killing vector fields are continuous isometries of the manifold. This means that the flow generates a symmetry, in the sense that moving each point of an object the same distance in the direction of the ''Killing vector'' will not distort distances on the object. Definition Specifically, a vector field X is a Killing vector field if the Lie derivative with respect to X of the metric tensor g vanishes: : \mathcal_ g = 0 \,. In terms of the Levi-Civita connection, this is : g\left(\nabla_Y X, Z\right) + g\left(Y, \nabla_Z X\right) = 0 for all vectors Y and . In local coordinates, this amounts to the Killing equation : \nabla_\mu X_\nu + \nabla_ X_\mu = 0 \,. This condition is expressed in covarian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Light-like
In mathematical physics, the causal structure of a Lorentzian manifold describes the possible causal relationships between points in the manifold. Lorentzian manifolds can be classified according to the types of causal structures they admit (''causality conditions''). Introduction In modern physics (especially general relativity) spacetime is represented by a Lorentzian manifold. The causal relations between points in the manifold are interpreted as describing which events in spacetime can influence which other events. The causal structure of an arbitrary (possibly curved) Lorentzian manifold is made more complicated by the presence of curvature. Discussions of the causal structure for such manifolds must be phrased in terms of smooth curves joining pairs of points. Conditions on the tangent vectors of the curves then define the causal relationships. Tangent vectors If \,(M,g) is a Lorentzian manifold (for metric g on manifold M) then the nonzero tangent vectors at each p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Invariance
In a relativistic theory of physics, a Lorentz scalar is a scalar expression whose value is invariant under any Lorentz transformation. A Lorentz scalar may be generated from, e.g., the scalar product of vectors, or by contracting tensors. While the components of the contracted quantities may change under Lorentz transformations, the Lorentz scalars remain unchanged. A simple Lorentz scalar in Minkowski spacetime is the ''spacetime distance'' ("length" of their difference) of two fixed events in spacetime. While the "position"-4-vectors of the events change between different inertial frames, their spacetime distance remains invariant under the corresponding Lorentz transformation. Other examples of Lorentz scalars are the "length" of 4-velocities (see below), or the Ricci curvature in a point in spacetime from general relativity, which is a contraction of the Riemann curvature tensor there. Simple scalars in special relativity Length of a position vector In special rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closed String Light Cone Vertex
Closed may refer to: Mathematics * Closure (mathematics), a set, along with operations, for which applying those operations on members always results in a member of the set * Closed set, a set which contains all its limit points * Closed interval, an interval which includes its endpoints * Closed line segment, a line segment which includes its endpoints * Closed manifold, a compact manifold which has no boundary * Closed differential form, a differential form whose exterior derivative is 0 Sport * Closed tournament, a competition open to a limited category of players * Closed (poker), a betting round where no player will have the right to raise Other uses * ''Closed'' (album), a 2010 album by Bomb Factory * Closed GmbH, a German fashion brand * Closed class, in linguistics, a class of words or other entities which rarely changes See also * * Close (other) * Closed loop (other) * Closing (other) * Closure (other) * Open (other) Ope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Light Cone String Propagator
Light, visible light, or visible radiation is electromagnetic radiation that can be perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahertz. The visible band sits adjacent to the infrared (with longer wavelengths and lower frequencies) and the ultraviolet (with shorter wavelengths and higher frequencies), called collectively '' optical radiation''. In physics, the term "light" may refer more broadly to electromagnetic radiation of any wavelength, whether visible or not. In this sense, gamma rays, X-rays, microwaves and radio waves are also light. The primary properties of light are intensity, propagation direction, frequency or wavelength spectrum, and polarization. Its speed in vacuum, , is one of the fundamental constants of nature. All electromagnetic radiation exhibits some properties of both particles and waves. Sin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bosonic String Theory
Bosonic string theory is the original version of string theory, developed in the late 1960s. It is so called because it contains only bosons in the spectrum. In the 1980s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory (supersymmetric string theory) became the real focus. Nevertheless, bosonic string theory remains a very useful model to understand many general features of perturbative string theory, and many theoretical difficulties of superstrings can actually already be found in the context of bosonic strings. Problems Although bosonic string theory has many attractive features, it falls short as a viable physical model in two significant areas. First, it predicts only the existence of bosons whereas many physical particles are fermions. Second, it predicts the existence of a mode of the string with imaginary mass, implying that the theory has an instability to a process known as "tachyon conde ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Keiji Kikkawa
was a Japanese theoretical physicist. Kikkawa received his bachelor's degree from Tokyo Metropolitan University in 1959, and a PhD from the University of Tokyo in 1964. After that he conducted research at the University of Tokyo, the University of Rochester and the University of Wisconsin. From 1970 he was associate professor at City College of New York and from 1974 at the Osaka University. From 1979 he was professor at Hiroshima University. In 1983 he returned to Osaka University where he worked until 1993. Between 2000 and 2004 he was a professor at Kanagawa University. Kikkawa is one of the pioneers of string theory, on which he worked since the late 1960s in collaboration with Bunji Sakita, Miguel Virasoro and Michio Kaku. Awards He was awarded the Nishina Memorial Prize The is the oldest and most prestigious physics award in Japan. Information Since 1955, the Nishina Memorial Prize has been awarded annually by the Nishina Memorial Foundation. The Foundation was e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michio Kaku
Michio Kaku (; ; born January 24, 1947) is an American theoretical physicist, Science communication, science communicator, futurologist, and writer of popular-science. He is a professor of theoretical physics at the City College of New York and the CUNY Graduate Center. Kaku is the author of several books about physics and related topics and has made frequent appearances on radio, television, and film. He is also a regular contributor to his own blog, as well as other popular media outlets. For his efforts to bridge science and science fiction, he is a 2021 Sir Arthur Clarke Award, Sir Arthur Clarke Lifetime Achievement Awardee. His books ''Physics of the Impossible'' (2008), ''Physics of the Future'' (2011), ''The Future of the Mind'' (2014), and The God Equation, ''The God Equation: The Quest for a Theory of Everything'' (2021) became The New York Times Best Seller list, ''New York Times'' best sellers. Kaku has hosted several television specials for the BBC, the Discovery Chan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Henry Schwarz
John Henry Schwarz ( ; born November 22, 1941) is an American theoretical physicist. Along with Yoichiro Nambu, Holger Bech Nielsen, Joël Scherk, Gabriele Veneziano, Michael Green, and Leonard Susskind, he is regarded as one of the founders of string theory. Early life and education He studied mathematics at Harvard College ( A.B., 1962) and theoretical physics at the University of California at Berkeley ( Ph.D., 1966), where his graduate advisor was Geoffrey Chew. For several years he was one of the very few physicists who pursued string theory as a viable theory of quantum gravity. His work with Michael Green on anomaly cancellation in Type I string theories led to the so-called " first superstring revolution" of 1984, which greatly contributed to moving string theory into the mainstream of research in theoretical physics. Schwarz was an assistant professor at Princeton University from 1966 to 1972. He then moved to the California Institute of Technology (Caltech), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Green (physicist)
Michael Boris Green (born 22 May 1946) is a British physicist and a pioneer of string theory. He is a professor of theoretical physics in the School of Physics and Astronomy at Queen Mary University of London, emeritus professor in the Department of Applied Mathematics and Theoretical Physics and a Fellow of Clare Hall, Cambridge. He was Lucasian Professor of Mathematics from 2009 to 2015. Early life and education Green was born the son of Genia Green and Absalom Green. He attended William Ellis School in London and Churchill College, Cambridge where he graduated with a Bachelor of Arts with first class honours in theoretical physics (1967) and a PhD in elementary particle theory (1970). Career Following his PhD, Green did postdoctoral research at Princeton University (1970–72), Cambridge and the University of Oxford. Between 1978 and 1993 he was a Lecturer and Professor at Queen Mary College, University of London, and in July 1993 he was appointed John Humphrey Plu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
