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Bondi–Metzner–Sachs Group
In gravitational theory, the Bondi–Metzner–Sachs (BMS) group, or the Bondi–van der Burg–Metzner–Sachs group, is an asymptotic symmetry group of asymptotically flat, Lorentzian spacetimes at null (''i.e.'', light-like) infinity. It was originally formulated in 1962 by Hermann Bondi, M. G. van der Burg, A. W. Metzner and Rainer K. Sachs in order to investigate the flow of energy at infinity due to propagating gravitational waves. Half a century later, this work of Bondi, van der Burg, Metzner, and Sachs is considered pioneering and seminal. In his autobiography, Bondi considered the 1962 work as his "best scientific work". 1962 work of Bondi, van der Burg, Metzner, and Sachs To give some context for the general reader, the naive expectation for asymptotically flat spacetime symmetries, ''i.e.'', symmetries of spacetime seen by observers located far away from all sources of the gravitational field, might be to extend and reproduce the symmetries of flat spacetime of sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry Group
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient space which takes the object to itself, and which preserves all the relevant structure of the object. A frequent notation for the symmetry group of an object ''X'' is ''G'' = Sym(''X''). For an object in a metric space, its symmetries form a subgroup of the isometry group of the ambient space. This article mainly considers symmetry groups in Euclidean geometry, but the concept may also be studied for more general types of geometric structure. Introduction We consider the "objects" possessing symmetry to be geometric figures, images, and patterns, such as a wallpaper pattern. For symmetry of physical objects, one may also take their physical composition as part of the pattern. (A pattern may be specified formally as a scalar field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel. The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. Definition An abelian group is a set A, together with an operation \cdot that combines any two elements a and b of A to form another element of A, denoted a \cdot b. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling. Although these two meanings of "symmetry" can sometimes be told apart, they are intricately related, and hence are discussed together in this article. Mathematical symmetry may be observed with respect to the passage of time; as a spatial relationship; through geometric transformations; through other kinds of functional transformations; and as an aspect of abstract objects, including theoretic models, language, and music. This article describes symmetry from three perspectives: in mathematics, including geometry, the most familiar type of symmetry for many people; in science and n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Waves
Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as waves similar to electromagnetic waves but the gravitational equivalent. Gravitational waves were later predicted in 1916 by Albert Einstein on the basis of his general theory of relativity as ripples in spacetime. Later he refused to accept gravitational waves. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously (at infinite speed)showing one of the ways the methods of Newtonian physics are unable to explain ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steven Weinberg
Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles. He held the Josey Regental Chair in Science at the University of Texas at Austin, where he was a member of the Physics and Astronomy Departments. His research on elementary particles and physical cosmology was honored with numerous prizes and awards, including the 1979 Nobel Prize in physics and the 1991 National Medal of Science. In 2004, he received the Benjamin Franklin Medal of the American Philosophical Society, with a citation that said he was "considered by many to be the preeminent theoretical physicist alive in the world today." He was elected to the U.S. National Academy of Sciences, Britain's Royal Society, the American Philosophical Society, and the American Academy of Arts and Sciences. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ward Identities
Ward may refer to: Division or unit * Hospital ward, a hospital division, floor, or room set aside for a particular class or group of patients, for example the psychiatric ward * Prison ward, a division of a penal institution such as a prison * Ward (electoral subdivision), electoral district or unit of local government ** Ward (KPK), local government in Khyber Pakhtunkhwa, Pakistan ** Ward (South Africa) ** Wards of Bangladesh ** Wards of Germany ** Wards of Japan ** Wards of Myanmar ** Wards and electoral divisions of the United Kingdom ** Ward (United States) *** Wards of New Orleans * Ward (fortification), part of a castle * Ward (LDS Church), a local congregation of The Church of Jesus Christ of Latter-day Saints * Ward (Vietnam), a type of third-tier subdivision of Vietnam Entertainment, arts and media * WOUF (AM), a radio station (750 AM) licensed to serve Petoskey, Michigan, United States, which held the call sign WARD from 2008 to 2021 * Ward Cleaver, a fictional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graviton
In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity. In string theory, believed by some to be a consistent theory of quantum gravity, the graviton is a massless state of a fundamental string. If it exists, the graviton is expected to be massless because the gravitational force has a very long range, and appears to propagate at the speed of light. The graviton must be a spin-2 boson because the source of gravitation is the stress–energy tensor, a second-order tensor (compared with electromagnetism's spin-1 photon, the source of which is the four-current, a first-order tensor). Additionally, it can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-matrix
In physics, the ''S''-matrix or scattering matrix relates the initial state and the final state of a physical system undergoing a scattering process. It is used in quantum mechanics, scattering theory and quantum field theory (QFT). More formally, in the context of QFT, the ''S''-matrix is defined as the unitary matrix connecting sets of asymptotically free particle states (the ''in-states'' and the ''out-states'') in the Hilbert space of physical states. A multi-particle state is said to be ''free'' (non-interacting) if it transforms under Lorentz transformations as a tensor product, or ''direct product'' in physics parlance, of ''one-particle states'' as prescribed by equation below. ''Asymptotically free'' then means that the state has this appearance in either the distant past or the distant future. While the ''S''-matrix may be defined for any background (spacetime) that is asymptotically solvable and has no event horizons, it has a simple form in the case of the Minkow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Field Theory
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. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the Lagrangian, a functional of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory in quantum mechanics. History Quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its devel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soft Graviton Theorem
In physics, the soft graviton theorem, first formulated by Steven Weinberg in 1965, allows calculation of the S-matrix, used in calculating the outcome of collisions between particles, when low-energy (soft) gravitons come into play. Specifically, if in a collision between ''n'' incoming particles from which ''m'' outgoing particles arise, the outcome of the collision depends on a certain ''S'' matrix, by adding one or more gravitons to the ''n'' + ''m'' particles, the resulting ''S'' matrix (let it be ''S''') differs from the initial ''S'' only by a factor that does not depend in any way, except for the momentum, on the type of particles to which the gravitons couple. The theorem also holds by putting photons in place of gravitons, thus obtaining a corresponding soft photon theorem. The theorem is used in the context of attempts to formulate a theory of quantum gravity in the form of a perturbative quantum theory, that is, as an approximation of a possible, as yet unknown ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew Strominger
Andrew Eben Strominger (; born 1955) is an American theoretical physicist who is the director of Harvard's Center for the Fundamental Laws of Nature. He has made significant contributions to quantum gravity and string theory. These include his work on Calabi–Yau compactification and topology change in string theory, and on the stringy origin of black hole entropy. He is a senior fellow at the Society of Fellows, and is the Gwill E. York Professor of Physics. Education Strominger received his bachelor's degree at Harvard College in 1977 and his master's degree at the University of California, Berkeley. He then received his PhD at MIT in 1982 under the supervision of Roman Jackiw. Prior to joining Harvard as a professor in 1997, he held a faculty position at the University of California, Santa Barbara. He is the author of over 200 publications. Research Notable contributions * a paper with Cumrun Vafa that explains the microscopic origin of the black hole entro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational-wave Astronomy
Gravitational-wave astronomy is an emerging branch of observational astronomy which aims to use gravitational waves (minute distortions of spacetime predicted by Albert Einstein's theory of general relativity) to collect observational data about objects such as neutron stars and black holes, events such as supernovae, and processes including those of the early universe shortly after the Big Bang. Gravitational waves have a solid theoretical basis, founded upon the theory of relativity. They were first predicted by Einstein in 1916; although a specific consequence of general relativity, they are a common feature of all theories of gravity that obey special relativity. However, after 1916 there was a long debate whether the waves were actually physical, or artefacts of coordinate freedom in general relativity; this was not fully resolved until the 1950s. Indirect observational evidence for their existence first came in the late 1980s, from the monitoring of the Hulse–Taylor bin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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