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Karl-Henning Rehren
Karl-Henning Rehren (born 1956 in Celle) is a German physicist who focuses on algebraic quantum field theory. Biography Rehren studied physics in Heidelberg, Paris and Freiburg. In Freiburg he received his PhD (advisor Klaus Pohlmeyer) in 1984. Habilitation 1991 in Berlin. Since 1997 he teaches physics in Göttingen. He became notable outside his field, especially among string theorists, in 1999 when he discovered the Algebraic holography (also called '' Rehren duality''), a relation between quantum field theories AdSd+1 and conformal quantum field theories on d-dimensional Minkowski spacetime, which is similar in scope to the Holographic principle. This work has no direct relation to the more well known Maldacena duality, but refers to the more general statement of the AdS/CFT correspondence by Edward Witten. It is generally accepted that the relation found by Rehren does not provide a proof for Witten's conjecture and is thus considered an independent result. Selected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Klaus Fredenhagen
Klaus Fredenhagen (born 1 December 1947) is a German theoretical physicist who works on the mathematical foundations of quantum field theory. Biography Klaus Fredenhagen was born on 1 December 1947 in Celle, a German city in Lower Saxony. He graduated in 1976 from the University of Hamburg under the supervision of Gert Roepstorff and Rudolf Haag. In 1985 he became a privatdozent and in 1990 a full professor at the second theory institute of the Hamburg University. Since 2013 he has been a professor emeritus and has continued to be active in research. Scientific career His research interests are algebraic quantum field theory and quantum field theory in curved spacetime. In 1981 he proved the existence of antiparticles in massive quantum field theories without using the CPT-invariance. In 1990 he and Rudolf Haag made important contributions to the understanding of the Hawking radiation of black holes on a rigorous mathematical footing. In 1994, together with Sergio Dopliche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heidelberg
Heidelberg (; Palatine German language, Palatine German: ''Heidlberg'') is a city in the States of Germany, German state of Baden-Württemberg, situated on the river Neckar in south-west Germany. As of the 2016 census, its population was 159,914, of which roughly a quarter consisted of students. Located about south of Frankfurt, Heidelberg is the List of cities in Baden-Württemberg by population, fifth-largest city in Baden-Württemberg. Heidelberg is part of the densely populated Rhine-Neckar, Rhine-Neckar Metropolitan Region. Heidelberg University, founded in 1386, is Germany's oldest and one of Europe's most reputable universities. Heidelberg is a Science, scientific hub in Germany and home to several internationally renowned #Research, research facilities adjacent to its university, including the European Molecular Biology Laboratory and four Max Planck Society, Max Planck Institutes. The city has also been a hub for the arts, especially literature, throughout the centurie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Local Quantum Physics
Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework for quantum field theory, because it was introduced by . The axioms are stated in terms of an algebra given for every open set in Minkowski space, and mappings between those. Haag–Kastler axioms Let \mathcal be the set of all open and bounded subsets of Minkowski space. An algebraic quantum field theory is defined via a net \_ of von Neumann algebras \mathcal(O) on a common Hilbert space \mathcal satisfying the following axioms: * ''Isotony'': O_1 \subset O_2 implies \mathcal(O_1) \subset \mathcal(O_2). * ''Causality'': If O_1 is space-like separated from O_2, then mathcal(O_1),\mathcal(O_2)0. * ''Poincaré covariance'': A strongly continuous unitary representation U(\mathcal) of the Poincaré group \mathcal on \mathcal exists such that \mathcal(gO) = U(g) \mathcal(O) U(g)^*, g \in \mathcal. * ''Spectrum condition'': ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Field Theory
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points. Scale invariance vs conformal invariance In quantum field theory, scale invariance is a common and natural symmetry, because any fixed point of the renormalization group is by definition scale invariant. Conformal symmetry is stronger than scale invariance, and one needs additional assumptions to argue that it should appear in nature. The basic idea behind its plausibility is that ''local'' scale invariant theories have their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiomatic Quantum Field Theory
Axiomatic quantum field theory is a mathematical discipline which aims to describe quantum field theory in terms of rigorous axioms. It is strongly associated with functional analysis and operator algebras, but has also been studied in recent years from a more geometric and functorial perspective. There are two main challenges in this discipline. First, one must propose a set of axioms which describe the general properties of any mathematical object that deserves to be called a "quantum field theory". Then, one gives rigorous mathematical constructions of examples satisfying these axioms. Analytic approaches Wightman axioms The first set of axioms for quantum field theories, known as the Wightman axioms, were proposed by Arthur Wightman in the early 1950s. These axioms attempt to describe QFTs on flat Minkowski spacetime by regarding quantum fields as operator-valued distributions acting on a Hilbert space. In practice, one often uses the Wightman reconstruction theorem, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edward Witten
Edward Witten (born August 26, 1951) is an American mathematical and theoretical physicist. He is a Professor Emeritus in the School of Natural Sciences at the Institute for Advanced Study in Princeton. Witten is a researcher in string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics. Witten's work has also significantly impacted pure mathematics. In 1990, he became the first physicist to be awarded a Fields Medal by the International Mathematical Union, for his mathematical insights in physics, such as his 1981 proof of the positive energy theorem in general relativity, and his interpretation of the Jones invariants of knots as Feynman integrals. He is considered the practical founder of M-theory.Duff 1998, p. 65 Early life and education Witten was born on August 26, 1951, in Baltimore, Maryland, to a Jewish family. He is the son of Lorraine (née Wollach) Witten and Louis Witten, a theoretical physicist specializing in gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AdS/CFT Correspondence
In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) which are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories (CFT) which are quantum field theories, including theories similar to the Yang–Mills theories that describe elementary particles. The duality represents a major advance in the understanding of string theory and quantum gravity.de Haro et al. 2013, p. 2 This is because it provides a non-perturbative formulation of string theory with certain boundary conditions and because it is the most successful realization of the holographic principle, an idea in quantum gravity originally proposed by Gerard 't Hooft and promoted by Leonard Susskind. It also provides a powerf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Juan Maldacena
Juan Martín Maldacena (born September 10, 1968) is an Argentine theoretical physicist and the Carl P. Feinberg Professor in the School of Natural Sciences at the Institute for Advanced Study, Princeton. He has made significant contributions to the foundations of string theory and quantum gravity. His most famous discovery is the AdS/CFT correspondence, a realization of the holographic principle in string theory. Biography Maldacena obtained his ''licenciatura'' (a six-year degree) in 1991 at the Instituto Balseiro, Bariloche, Argentina, under the supervision of Gerardo Aldazábal. He then obtained his Ph.D. in physics at Princeton University after completing a doctoral dissertation titled "Black holes in string theory" under the supervision of Curtis Callan in 1996, and went on to a post-doctoral position at Rutgers University. In 1997, he joined Harvard University as associate professor, being quickly promoted to Professor of Physics in 1999. Since 2001 he has been a professor a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holographic Principle
The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a light-like boundary like a gravitational horizon. First proposed by Gerard 't Hooft, it was given a precise string-theory interpretation by Leonard Susskind, who combined his ideas with previous ones of 't Hooft and Charles Thorn. Leonard Susskind said, “The three-dimensional world of ordinary experience––the universe filled with galaxies, stars, planets, houses, boulders, and people––is a hologram, an image of reality coded on a distant two-dimensional surface." As pointed out by Raphael Bousso, Thorn observed in 1978 that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the AdS/CFT correspondence. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Spacetime
In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be implied by the postulates of special relativity. Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time may differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events.This makes spacetime distance an invariant. Becau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Field Theory
A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points. Scale invariance vs conformal invariance In quantum field theory, scale invariance is a common and natural symmetry, because any fixed point of the renormalization group is by definition scale invariant. Conformal symmetry is stronger than scale invariance, and one needs additional assumptions to argue that it should appear in nature. The basic idea behind its plausibility is that ''local'' scale invariant theories have their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Holography
Algebraic holography, also sometimes called Rehren duality, is an attempt to understand the holographic principle of quantum gravity within the framework of algebraic quantum field theory, due to Karl-Henning Rehren. It is sometimes described as an alternative formulation of the AdS/CFT correspondence of string theory, but some string theorists reject this statemen The theories discussed in algebraic holography do not satisfy the usual holographic principle because their entropy follows a higher-dimensional power law. Rehren's duality The conformal boundary of an anti-de Sitter space (or its universal covering space) is the conformal Minkowski space (or its universal covering space) with one fewer dimension. Let's work with the universal covering spaces. In AQFT, a QFT in the conformal space is given by a conformally covariant net of C* algebras over the conformal space and the QFT in AdS is given a covariant net of C* algebras over AdS. Any two distinct null geodesic hypersurfa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
