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Spinfoam
In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity. These structures are employed in loop quantum gravity as a version of quantum foam. In loop quantum gravity The covariant formulation of loop quantum gravity provides the best formulation of the dynamics of the theory of quantum gravity – a quantum field theory where the invariance under diffeomorphisms of general relativity applies. The resulting path integral represents a sum over all the possible configurations of spin foam. Spin network A spin network is a one-dimensional graph, together with labels on its vertices and edges which encode aspects of a spatial geometry. A spin network is defined as a diagram like the Feynman diagram which makes a basis of connections between the elements of a differentiable manifold for the Hilbert spa ... [...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] |
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] |
Group Field Theory
Group field theory (GFT) is a quantum field theory in which the base manifold is taken to be a Lie group. It is closely related to background independent quantum gravity approaches such as loop quantum gravity, the spin foam formalism and causal dynamical triangulation. It can be shown that its perturbative expansion can be interpreted as spin foams and simplicial pseudo-manifolds (depending on the representation of the fields). Thus, its partition function defines a non-perturbative sum over all simplicial topologies and geometries, giving a path integral formulation of quantum spacetime. See also *Shape dynamics * Causal Sets * Fractal cosmology * Loop quantum gravity * Planck scale * Quantum gravity *Regge calculus * Simplex *Simplicial manifold *Spin foam In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop Quantum Gravity
Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force. As a theory LQG postulates that the structure of Spacetime, space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale above the order of a Planck length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic hypothesis, atomic structure. The areas of research, which involves about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop Quantum Gravity
Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force. As a theory LQG postulates that the structure of Spacetime, space and time is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called spin networks. The evolution of a spin network, or spin foam, has a scale above the order of a Planck length, approximately 10−35 meters, and smaller scales are meaningless. Consequently, not just matter, but space itself, prefers an atomic hypothesis, atomic structure. The areas of research, which involves about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feynman's Path Integral
The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization. Unlike previous methods, the path integral allows one to easily change coordinates between very different canonical descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions of a certain type, these are ''coordinate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum History
In quantum mechanics, the consistent histories (also referred to as decoherent histories) approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology. This interpretation of quantum mechanics is based on a consistency criterion that then allows probabilities to be assigned to various alternative histories of a system such that the probabilities for each history obey the rules of classical probability while being consistent with the Schrödinger equation. In contrast to some interpretations of quantum mechanics, particularly the Copenhagen interpretation, the framework does not include "wavefunction collapse" as a relevant description of any physical process, and emphasizes that measurement theory is not a fundamental ingredient of quantum mechanics. Histories A ''homogeneous history'' H_i (here i labels different histories) is a sequence of Propositio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topological
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a ''topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connecte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jerzy Lewandowski
Jerzy Lewandowski is a Polish theoretical physicist who studies quantum gravity. He is a professor of physics at the University of Warsaw. Lewandowski received his doctorate in Warsaw under Andrzej Trautman. He worked closely with Abhay Ashtekar at Pennsylvania State University in the 1990s on the mathematical justification of Loop Quantum Gravity (LQG). Among other things, he was at the Erwin Schrödinger Institute in Vienna and at the Max Planck Institute for Gravitational Physics in Golm near Potsdam. He dealt with cosmological models and the entropy of black holes in the LQG. In 2010 he and his colleagues investigated a scalar field together with the gravitational field as part of LQG and were able to show the origin of a time as the ratio of the scalar to the gravitational field, and the quantization of the gravitational field. Publications * With Ashtekar ''Background independent quantum gravity: a status report'', Classical and Quantum Gravity, Band 21, 2004, R 5Arxi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laurent Freidel
Laurent Freidel is a French theoretical physicist and mathematical physicist known mainly for his contributions to quantum gravity, including loop quantum gravity, spin foam models, doubly special relativity, group field theory, relative locality and most recently metastring theory. He is currently a faculty member at Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada. Freidel received his PhD in 1994 from the École normale supérieure de Lyon (ENSL) in Lyon, France. He stayed at ENSL officially as a research scientist for 12 years, until 2006. During that time he also held a postdoctoral position at Pennsylvania State University in State College, Pennsylvania, United States from 1997 to 1999 and an adjunct professor position at the University of Waterloo in Waterloo, Ontario, Canada from 2002 to 2009. In 2006 he joined Perimeter Institute as its ninth faculty member. Between 2004 and 2006 Freidel has coauthored a series of papers on the Ponzano-Regge mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barrett–Crane Model
The Barrett–Crane model is a model in quantum gravity, first published in 1998, which was defined using the Plebanski action. The B field in the action is supposed to be a so(3, 1)-valued 2-form, i.e. taking values in the Lie algebra of a special orthogonal group. The term :B^ \wedge B^ in the action has the same symmetries as it does to provide the Einstein–Hilbert action. But the form of :B^ is not unique and can be posed by the different forms: *\pm e^i \wedge e^j *\pm \epsilon^ e_k \wedge e_l where e^i is the tetrad and \epsilon^ is the antisymmetric symbol of the so(3, 1)-valued 2-form fields. The Plebanski action can be constrained to produce the BF model which is a theory of no local degrees of freedom. John W. Barrett and Louis Crane modeled the analogous constraint on the summation over spin foam. The Barrett–Crane model on spin foam quantizes the Plebanski action, but its path integral amplitude corresponds to the degenerate B field and not the specif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tullio Regge
Tullio Eugenio Regge (; July 11, 1931 – October 23, 2014) was an Italian theoretical physicist. Biography Regge obtained the ''laurea'' in physics from the University of Turin in 1952 under the direction of Mario Verde and Gleb Wataghin, and a PhD in physics from the University of Rochester in 1957 under the direction of Robert Marshak. From 1958 to 1959 Regge held a post at the Max Planck Institute for Physics where he worked with Werner Heisenberg. In 1961 he was appointed to the chair of Relativity at the University of Turin. He also held an appointment at the Institute for Advanced Study from 1965 to 1979. He was emeritus professor at the Polytechnic University of Turin while contributing work at CERN as a visiting scientist. Regge died on October 23, 2014. He was married to Rosanna Cester, physicist, by whom he had three children: Daniele, Marta and Anna. In 1959, Regge discovered a mathematical property of potential scattering in the Schrödinger equation—that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
