|
CGHS Model
The Callan–Giddings–Harvey–Strominger model or CGHS model in short is a toy model of general relativity in 1 spatial and 1 time dimension. Overview General relativity is a highly nonlinear model, and as such, its 3+1D version is usually too complicated to analyze in detail. In 3+1D and higher, propagating gravitational waves exist, but not in 2+1D or 1+1D. In 2+1D, general relativity becomes a topological field theory with no local degrees of freedom, and all 1+1D models are locally flat. However, a slightly more complicated generalization of general relativity which includes dilatons will turn the 2+1D model into one admitting mixed propagating dilaton-gravity waves, as well as making the 1+1D model geometrically nontrivial locally. The 1+1D model still does not admit any propagating gravitational (or dilaton) degrees of freedom, but with the addition of matter fields, it becomes a simplified, but still nontrivial model. With other numbers of dimensions, a dilaton-gravity co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toy Model
In the modeling of physics, a toy model is a deliberately simplistic model with many details removed so that it can be used to explain a mechanism concisely. It is also useful in a description of the fuller model. * In "toy" mathematical models, this is usually done by reducing or extending the number of dimensions or reducing the number of fields/variables or restricting them to a particular symmetric form. * In Macroeconomics modelling, are a class of models, some may be only loosely based on theory, others more explicitly so. But they have the same purpose. They allow for a quick first pass at some question, and present the essence of the answer from a more complicated model or from a class of models. For the researcher, they may come before writing a more elaborate model, or after, once the elaborate model has been worked out. Blanchard list of examples includes IS–LM model, the Mundell–Fleming model, the RBC model, and the New Keynesian model. * In "toy" physical descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-critical String Theory
The non-critical string theory describes the relativistic string without enforcing the critical dimension. Although this allows the construction of a string theory in 4 spacetime dimensions, such a theory usually does not describe a Lorentz invariant background. However, there are recent developments which make possible Lorentz invariant quantization of string theory in 4-dimensional Minkowski space-time. There are several applications of the non-critical string. Through the AdS/CFT correspondence it provides a holographic description of gauge theories which are asymptotically free. It may then have applications to the study of the QCD, the theory of strong interactions between quarks. Another area of much research is two-dimensional string theory which provides simple toy models of string theory. There also exists a duality to the 3-dimensional Ising model. The critical dimension and central charge In order for a string theory to be consistent, the worldsheet theory must be ... [...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] |
Quantum Gravity
Quantum gravity (QG) is a field of theoretical physics that seeks to describe gravity according to the principles of quantum mechanics; it deals with environments in which neither gravitational nor quantum effects can be ignored, such as in the vicinity of black holes or similar compact astrophysical objects, such as neutron stars. Three of the four fundamental forces of physics are described within the framework of quantum mechanics and quantum field theory. The current understanding of the fourth force, gravity, is based on Albert Einstein's general theory of relativity, which is formulated within the entirely different framework of classical physics. However, that description is incomplete: describing the gravitational field of a black hole in the general theory of relativity leads physical quantities, such as the spacetime curvature, to diverge at the center of the black hole. This signals the breakdown of the general theory of relativity and the need for a theory that goes b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Black Hole Information Paradox
The black hole information paradox is a puzzle that appears when the predictions of quantum mechanics and general relativity are combined. The theory of general relativity predicts the existence of black holes that are regions of spacetime from which nothing — not even light — can escape. In the 1970s, Stephen Hawking applied the rules of quantum mechanics to such systems and found that an isolated black hole would emit a form of radiation called Hawking radiation. Hawking also argued that the detailed form of the radiation would be independent of the initial state of the black hole and would depend only on its mass, electric charge and angular momentum. The information paradox appears when one considers a process in which a black hole is formed through a physical process and then evaporates away entirely through Hawking radiation. Hawking's calculation suggests that the final state of radiation would retain information only about the total mass, electric charge and angular m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Action
In quantum field theory, the quantum effective action is a modified expression for the classical action taking into account quantum corrections while ensuring that the principle of least action applies, meaning that extremizing the effective action yields the equations of motion for the vacuum expectation values of the quantum fields. The effective action also acts as a generating functional for one-particle irreducible correlation functions. The potential component of the effective action is called the effective potential, with the expectation value of the true vacuum being the minimum of this potential rather than the classical potential, making it important for studying spontaneous symmetry breaking. It was first defined perturbatively by Jeffrey Goldstone and Steven Weinberg in 1962, while the non-perturbative definition was introduced by Bryce DeWitt in 1963 and independently by Giovanni Jona-Lasinio in 1964. The article describes the effective action for a single scalar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liouville Term
Joseph Liouville (; ; 24 March 1809 – 8 September 1882) was a French mathematician and engineer. Life and work He was born in Saint-Omer in France on 24 March 1809. His parents were Claude-Joseph Liouville (an army officer) and Thérèse Liouville (née Balland). Liouville gained admission into the École Polytechnique in 1825 and graduated in 1827. Just like Augustin-Louis Cauchy before him, Liouville studied engineering at École des Ponts et Chaussées after graduating from the Polytechnique, but opted instead for a career in mathematics. After some years as an assistant at various institutions including the École Centrale Paris, he was appointed as professor at the École Polytechnique in 1838. He obtained a chair in mathematics at the Collège de France in 1850 and a chair in mechanics at the Faculté des Sciences in 1857. Besides his academic achievements, he was very talented in organisational matters. Liouville founded the ''Journal de Mathématiques Pures et Ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Anomaly
A conformal anomaly, scale anomaly, trace anomaly or Weyl anomaly is an anomaly, i.e. a quantum phenomenon that breaks the conformal symmetry of the classical theory. A classically conformal theory is a theory which, when placed on a surface with arbitrary background metric, has an action that is invariant under rescalings of the background metric (Weyl transformations), combined with corresponding transformations of the other fields in the theory. A conformal quantum theory is one whose partition function is unchanged by rescaling the metric. The variation of the action with respect to the background metric is proportional to the stress tensor, and therefore the variation with respect to a conformal rescaling is proportional to the trace of the stress tensor. As a result, the trace of the stress tensor must vanish for a conformally invariant theory. In the presence of a conformal anomaly the trace of the stress tensor can nevertheless acquire a non-vanishing expectation. For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Causal Structure
In mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold. 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 point in the manifold can be classified into three disjoint types. A tangent vector X is: * timelike if \,g(X,X) 0 Here we use the ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liouville Gravity
In physics, Liouville field theory (or simply Liouville theory) is a two-dimensional conformal field theory whose classical equation of motion is a generalization of Liouville's equation. Liouville theory is defined for all complex values of the central charge c of its Virasoro symmetry algebra, but it is unitary only if :c\in(1,+\infty), and its classical limit is : c\to +\infty. Although it is an interacting theory with a continuous spectrum, Liouville theory has been solved. In particular, its three-point function on the sphere has been determined analytically. Introduction Liouville theory describes the dynamics of a field \phi called the Liouville field, which is defined on a two-dimensional space. This field is not a free field due to the presence of an exponential potential : V(\phi) = e^\ , where the parameter b is called the coupling constant. In a free field theory, the energy eigenvectors e^ are linearly independent, and the momentum \alpha is conserved in intera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jackiw–Teitelboim Gravity
The ''R'' = ''T'' model, also known as Jackiw–Teitelboim gravity (named after Roman Jackiw and Claudio Teitelboim), is a theory of gravity with dilaton coupling in one spatial and one time dimension. It should not be confused with the CGHS model or Liouville gravity. The action is given by :S = \frac\int d^2x\, \sqrt\, \Phi \left( R - \Lambda \right) The metric in this case is more amenable to analytical solutions than the general 3+1D case though a canonical reduction for the latter has recently been obtained. For example, in 1+1D, the metric for the case of two mutually interacting bodies can be solved exactly in terms of the Lambert W function, even with an additional electromagnetic field. By varying with respect to Φ, we get R=\Lambda on shell, which means the metric is either Anti-de Sitter space or De Sitter space In mathematical physics, ''n''-dimensional de Sitter space (often abbreviated to dS''n'') is a maximally symmetric Lorentzian manifold with constant posit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Reduction
Dimensional reduction is the limit of a compactified theory where the size of the compact dimension goes to zero. In physics, a theory in ''D'' spacetime dimensions can be redefined in a lower number of dimensions ''d'', by taking all the fields to be independent of the location in the extra ''D'' − ''d'' dimensions. For example, consider a periodic compact dimension with period ''L''. Let ''x'' be the coordinate along this dimension. Any field \phi can be described as a sum of the following terms: :\phi_n(x) = A_n \cos \left( \frac\right) with ''A''''n'' a constant. According to quantum mechanics, such a term has momentum ''nh''/''L'' along ''x'', where ''h'' is Planck's constant. Therefore, as L goes to zero, the momentum goes to infinity, and so does the energy, unless ''n'' = 0. However ''n'' = 0 gives a field which is constant with respect to ''x''. So at this limit, and at finite energy, \phi will not depend on ''x''. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
