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Smolin–Susskind Debate
Leonard Susskind (; born June 16, 1940)his 60th birthday was celebrated with a special symposium at Stanford University.in Geoffrey West's introduction, he gives Suskind's current age as 74 and says his birthday was recent. is an American physicist, who is a professor of theoretical physics at Stanford University, and founding director of the Stanford Institute for Theoretical Physics. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the US National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study. Susskind is widely regarded as one of the fathers of string theory. He was the first to give a precise string-theoretic interpretation of the holographic principle in 1995 and the first to introduce the idea of the stri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York City
New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the List of United States cities by population density, most densely populated major city in the United States, and is more than twice as populous as second-place Los Angeles. New York City lies at the southern tip of New York (state), New York State, and constitutes the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the world by urban area, urban landmass. With over 20.1 million people in its metropolitan statistical area and 23.5 million in its combined statistical area as of 2020, New York is one of the world's most populous Megacity, megacities, and over 58 million people live within of the city. New York City is a global city, global Culture of New ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Douglas Stanford
Douglas Stanford is an American theoretical physicist. He is an associate professor of physics at Stanford Institute for Theoretical Physics of Stanford University. His research interests include quantum gravity, quantum field theory and string theory. Stanford was awarded the 2018 New Horizons in Physics Prize by Fundamental Physics Prize Foundation for his work on improving the understanding of quantum mechanics of black holes via chaos theory. Early life and education Douglas Stanford was born in Anacortes, Washington. He attended Anacortes Senior High school. Stanford graduated from the Stanford University in 2009 with B.S. in physics and mathematics. He earned an M.S. in mathematics from the University of Cambridge in 2010. He earned his Ph.D. in physics in 2014 from Stanford University, under the guidance of Leonard Susskind. Career Research Stanford worked at Institute for Advanced Study, Princeton from September 2014 to April 2019 as a post-doctoral researcher. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Staggered Fermion
In lattice field theory, staggered fermions (also known as Kogut–Susskind fermions) are a fermion discretization that reduces the number of fermion doublers from sixteen to four. They are one of the fastest lattice fermions when it comes to simulations and they also possess some nice features such as a remnant chiral symmetry, making them very popular in lattice QCD calculations. Staggered fermions were first formulated by John Kogut and Leonard Susskind in 1975 and were later found to be equivalent to the discretized version of the Dirac–Kähler fermion. Constructing staggered fermions Single-component basis The naively discretized Dirac action in Euclidean spacetime with lattice spacing a and Dirac fields \psi_n at every lattice point, indexed by n = (n_1,n_2,n_3,n_4), takes the form : S = a^4 \sum_\bar \psi_n \bigg(\sum^4_\gamma_\mu \frac+m\psi_n\bigg). Staggered fermions are constructed from this by performing the staggered transformation into a new basis of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Susskind–Glogower Operator
The Susskind–Glogower operator, first proposed by Leonard Susskind and J. Glogower, refers to the operator where the phase is introduced as an approximate polar decomposition of the creation and annihilation operators. It is defined as : V=\fraca, and its adjoint : V^=a^\frac. Their commutation relation is : ,V^, 0\rangle\langle 0, , where , 0\rangle is the vacuum state of the harmonic oscillator. They may be regarded as a (exponential of) phase operator because : Va^a V^=a^a+1, where a^a is the number operator. So the exponential of the phase operator displaces the number operator in the same fashion as the momentum operator In quantum mechanics, the momentum operator is the operator (physics), operator associated with the momentum (physics), linear momentum. The momentum operator is, in the position representation, an example of a differential operator. For the case o ... acts as the generator of translations in quantum mechanics: \exp\left(i\frac\right)\hat\exp\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RST Model
The Russo–Susskind–Thorlacius model or RST model in short is a modification of the CGHS model to take care of conformal anomalies and render it analytically soluble. In the CGHS model, if we include Faddeev–Popov ghosts to gauge-fix diffeomorphisms in the conformal gauge, they contribute an anomaly of -24. Each matter field contributes an anomaly of 1. So, unless N=24, we will have gravitational anomalies In theoretical physics, a gravitational anomaly is an example of a gauge anomaly: it is an effect of quantum mechanics — usually a one-loop diagram—that invalidates the general covariance of a theory of general relativity combined with som .... To the CGHS action :S_ = \frac \int d^2x\, \sqrt\left\, the following term :S_ = - \frac \int d^2x\, \sqrt \left R\fracR - 2\phi R \right/math> is added, where ''κ'' is either (N-24)/12 or N/12 depending upon whether ghosts are considered. The nonlocal term leads to nonlocality. In the conformal gauge, :S_ = -\frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Worldsheet
In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind as a direct generalization of the world line concept for a point particle in special and general relativity. The type of string, the geometry of the spacetime in which it propagates, and the presence of long-range background fields (such as gauge fields) are encoded in a two-dimensional conformal field theory defined on the worldsheet. For example, the bosonic string in 26 dimensions has a worldsheet conformal field theory consisting of 26 free scalar bosons. Meanwhile, a superstring worldsheet theory in 10 dimensions consists of 10 free scalar fields and their fermionic superpartners. Mathematical formulation Bosonic string We begin with the classical formulation of the bosonic string. First fix a d-dimensional flat spacetime (d-dimensional Minkowski space), M, which serves as the ambient space for the string. A w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Theory Landscape
The string theory landscape or landscape of vacua refers to the collection of possible false vacua in string theory,The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See M. Douglas, "The statistics of string / M theory vacua", ''JHEP'' 0305, 46 (2003). ; S. Ashok and M. Douglas, "Counting flux vacua", ''JHEP'' 0401, 060 (2004). together comprising a collective "landscape" of choices of parameters governing compactifications. The term "landscape" comes from the notion of a fitness landscape in evolutionary biology. It was first applied to cosmology by Lee Smolin in his book '' The Life of the Cosmos'' (1997), and was first used in the context of string theory by Leonard Susskind. Compactified Calabi–Yau manifolds In string theory the number of flux vacua is commonly thought to be roughly 10^, but could be 10^ or higher. The large number of possibilities arises from choices of Calabi–Yau manifolds and choices of gen ... [...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] |
Matrix Theory (physics)
In theoretical physics, the BFSS matrix model or matrix theory is a quantum mechanical model proposed by Tom Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind in 1997. Overview This theory describes the behavior of a set of nine large matrices. In their original paper, these authors showed, among other things, that the low energy limit of this matrix model is described by eleven-dimensional supergravity. These calculations led them to propose that the BFSS matrix model is exactly equivalent to M-theory. The BFSS matrix model can therefore be used as a prototype for a correct formulation of M-theory and a tool for investigating the properties of M-theory in a relatively simple setting. The BFSS matrix model is also considered the worldvolume theory of a large number of D0-branes in Type IIA string theory. Noncommutative geometry In geometry, it is often useful to introduce coordinates. For example, in order to study the geometry of the Euclidean plane, one defines ... [...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] |
Hamiltonian Lattice Gauge Theory
In physics, Hamiltonian lattice gauge theory is a calculational approach to gauge theory and a special case of lattice gauge theory in which the space is discretized but time is not. The Hamiltonian is then re-expressed as a function of degrees of freedom defined on a d-dimensional lattice. Following Wilson, the spatial components of the vector potential are replaced with Wilson lines over the edges, but the time component is associated with the vertices. However, the temporal gauge is often employed, setting the electric potential to zero. The eigenvalues of the Wilson line operators U(e) (where e is the ( oriented) edge in question) take on values on the Lie group G. It is assumed that G is compact, otherwise we run into many problems. The conjugate operator to U(e) is the electric field E(e) whose eigenvalues take on values in the Lie algebra \mathfrak. The Hamiltonian receives contributions coming from the plaquettes (the magnetic contribution) and contributions coming from t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ER=EPR
ER = EPR is a conjecture in physics stating that two entangled particles (a so-called Einstein–Podolsky–Rosen or EPR pair) are connected by a wormhole (or Einstein–Rosen bridge) and is thought by some to be a basis for unifying general relativity and quantum mechanics into a theory of everything. Overview The conjecture was proposed by Leonard Susskind and Juan Maldacena in 2013. They proposed that a wormhole (Einstein–Rosen bridge or ER bridge) is equivalent to a pair of maximally entangled black holes. EPR refers to quantum entanglement (EPR paradox). The symbol is derived from the first letters of the surnames of authors who wrote the first paper on wormholes (Albert Einstein and Nathan Rosen) and the first paper on entanglement (Einstein, Boris Podolsky and Rosen). The two papers were published in 1935, but the authors did not claim any connection between the concepts. Conjectured resolution This is a conjectured resolution to the AMPS firewall paradox. Whether or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
