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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] |
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] |
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] |
Faddeev–Popov Ghost
In physics, Faddeev–Popov ghosts (also called Faddeev–Popov gauge ghosts or Faddeev–Popov ghost fields) are extraneous fields which are introduced into gauge quantum field theories to maintain the consistency of the path integral formulation. They are named after Ludvig Faddeev and Victor Popov. A more general meaning of the word 'ghost' in theoretical physics is discussed in Ghost (physics). Overcounting in Feynman path integrals The necessity for Faddeev–Popov ghosts follows from the requirement that quantum field theories yield unambiguous, non-singular solutions. This is not possible in the path integral formulation when a gauge symmetry is present since there is no procedure for selecting among physically equivalent solutions related by gauge transformation. The path integrals overcount field configurations corresponding to the same physical state; the measure of the path integrals contains a factor which does not allow obtaining various results directly from the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Gauge , in cartography
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Conformal may refer to: * Conformal (software), in ASIC Software * Conformal coating in electronics * Conformal cooling channel, in injection or blow moulding * Conformal field theory in physics, such as: ** Boundary conformal field theory ** Coset conformal field theory ** Logarithmic conformal field theory ** Rational conformal field theory * Conformal fuel tanks on military aircraft * Conformal hypergraph, in mathematics * Conformal geometry, in mathematics * Conformal group, in mathematics * Conformal map, in mathematics * Conformal map projection In cartography, a conformal map projection is one in which every angle between two curves that cross each other on Earth (a sphere or an ellipsoid) is preserved in the image of the projection, i.e. the projection is a conformal map in the mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Anomaly
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 some other fields. The adjective "gravitational" is derived from the symmetry of a gravitational theory, namely from general covariance. A gravitational anomaly is generally synonymous with ''diffeomorphism anomaly'', since general covariance is symmetry under coordinate reparametrization; i.e. diffeomorphism. General covariance is the basis of general relativity, the classical theory of gravitation. Moreover, it is necessary for the consistency of any theory of quantum gravity, since it is required in order to cancel unphysical degrees of freedom with a negative norm, namely gravitons polarized along the time direction. Therefore, all gravitational anomalies must cancel out. The anomaly usually appears as a Feynman diagram with a chiral fer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Action At A Distance
In physics, action at a distance is the concept that an object can be affected without being physically touched (as in mechanical contact) by another object. That is, it is the non-local interaction of objects that are separated in space. Non-contact forces is action at a distance affecting specifically an object's motion. This term was used most often in the context of early theories of gravity and electromagnetism to describe how an object responds to the influence of distant objects. For example, Coulomb's law and Newton's law of universal gravitation are such early theories. More generally, "action at a distance" describes the failure of early atomistic and mechanistic theories which sought to reduce all physical interaction to collision. The exploration and resolution of this problematic phenomenon led to significant developments in physics, from the concept of a field, to descriptions of quantum entanglement and the mediator particles of the Standard Model. Electrici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anomalies (physics)
Anomaly may refer to: Science Natural *Anomaly (natural sciences) **Atmospheric anomaly **Geophysical anomaly Medical *Congenital anomaly (birth defect), a disorder present at birth ** Physical anomaly, a deformation of an anatomical structure ***Congenital vertebral anomaly, any of several malformations of the spine **Collie eye anomaly, eye disease of dogs *** Coronary artery anomaly, a congenital abnormality in the heart ***Ebstein's anomaly, a congenital heart defect in which the opening of the tricuspid valve is displaced *** Uhl anomaly, a congenital heart disease affecting the myocardial muscle ***Vaginal anomalies Biology * Anomalous, a species of moth in the Noctuid family * Chromosome anomaly, a disorder caused by a structural error in a chromosome or an atypical number of chromosomes *Genetic anomaly, a disorder caused by mutation *Teratology, the study of developmental anomalies Physics *Anomalous diffusion is the movement of molecules from a region of lower conce ... [...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] |
