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Topic: Einstein-Cartan theory

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ScienceDaily: General relativity General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915. General relativity was developed by Einstein in a process that began in 1907 with the publication of an article on the influence of gravity and acceleration on the behavior of light in special relativity. In this theory, spacetime is treated as a 4-dimensional Lorentzian manifold which is curved by the presence of mass, energy, and momentum (or stress-energy) within it. www.sciencedaily.com /encyclopedia/general_relativity   (5224 words)

blagoj In the framework of Riemannian geometry Einstein's GR is expressed as a theory in which gravitational phenomena are related to the geometry of spacetime. A significant success of string theory in a consistent treatment of quantum gravity in the eighties led to a renewed interest for identifying the underlying symmetry principles of strings, and for the construction of the related covariant field theory. Theories of basic physical interactions, such as the electroweak theory or GR, are theories with gauge symmetries. www.chronotechnicsbank2.50megs.com /blagoj.html   (2868 words)

Laszlo -- Subtle Connections In the 1920s studies carried out by Albert Einstein and E. Cartan laid the foundation of the theory that became subsequent known as the ECT (Einstein- Cartan Theory). The torsion field theory takes a modified form of the original electron- positron model of the "Dirac- sea": the vacuum's energy field is viewed as a system of rotating wave packets of electrons and positrons (rather than a sea of electron- positron pairs). In his theory the vacuum's energy field has the properties of a superfluid. goertzel.org /dynapsyc/1996/subtle.html   (7425 words)

The world's top loop quantum gravity websites Mathematically, the theory is modelled after Riemann's metric geometry, but the Lorentz group of spacetime symmetries (an essential ingredient of Einstein's own theory of special relativity) replaces the group of rotational symmetries of space. Although string theory had its origins in the study of quark confinement and not of quantum gravity, it was soon discovered that the string spectrum contains the graviton, and that "condensation" of certain vibration modes of strings is equivalent to a modification of the original background. As a theory of quantum gravity, LQG is the main competitor of string theory, albeit a distant one: stringy people outnumber loopy people by a factor of roughly 10 and stringy papers outnumber loopy papers by a factor of roughly 50. dirs.org /wiki-article-tab.cfm/loop_quantum_gravity   (5682 words)

Cartan connection In mathematics the Cartan connection construction of differential geometry is a flexible generalisation of the concept based on an understanding of the of the affine group in the usual approach. Cartan formalism is an alternative approach to covariant derivatives and curvature using differential forms and frames. It was by Élie Cartan as part of (and a way formulating) his method of moving frames. www.freeglossary.com /Tetrad   (965 words)

Eotvos and Novel Equivalence Principle Tests A Poincaré group gauge theory can be equivalent to the Einstein-Cartan theory of gravitation[13]. It is a quirk of QCM graph theory analysis that 15 points input as *.xyz file format would require more than the age of the universe to calculate - to give the same answer as *.hin format input after a few minutes. Penelope Smith at Lehigh University notes that CHI is a connection between eigenvalues, special functions, and their representation theory with solid angles and exponentials of fractions of pi. www.mazepath.com /uncleal/eotvos.htm   (7763 words)

Riemannian Geometry, Kaluza-Klein Theories... It happens that, in many cases, the theory takes a simpler form if we assume that what we observe is just a shadow (projection) of something that takes place in space-time which has more than 4 dimensions. One of the aims of the present book is to present the geometrical and analytical aspects of "dimensional reduction" and to discuss with more generality several situations which have been considered in the past. The fact that we do not see the extra dimensions (those of the so called "internal space") can be described, if not explained, by the fact that the metric of our multidimensional universe singles out some directions along which it is invariant or at least equivariant (in some sense). quantumfuture.net /quantum_future/kkintro.htm   (897 words)

The Divine Cosmos, Chapter One: The Breakthroughs of Dr. N.A. Kozyrev In 1913, Dr. Eli Cartan was the first to clearly demonstrate that the “fabric” (flow) of space and time in Einstein’s general theory of relativity not only “curved”, but it also possessed a spinning or spiraling movement within itself known as “torsion.” This area of physics is typically referred to as Einstein-Cartan Theory, or ECT. We will begin with a preliminary discussion of Einstein’s theory of relativity, followed by Dr. Eli Cartan’s additions to the model, which first established the existence of torsion fields in theory. As we already mentioned, the Einstein-Cartan theory first established a theoretical basis for the existence of torsion fields in 1913. ascension2000.com /DivineCosmos/01.htm   (10176 words)

Cartan: a Mathematica package for tensor analysis It contains examples of how to find solutions to Einstein's field equations or to the field equations of the Einstein-Cartan theory, and also of how to calculate the renormalized stress-tensor in curved space-time. Cartan was developed in part at the European Centre for Nuclear Research (CERN) in Geneva and at the Nordic Institute for Theoretical Physics (NORDITA) in Copenhagen. Cartan is an easy-to-use tensor component package for interactive tensor calculations in general Riemann-Cartan spaces of arbitrary dimensions and signatures. www.adinfinitum.no /cartan   (642 words)

Einstein-Cartan Theory For the purpose of constitutive theory the Einstein-Cartan theory is the most suitable generalization of GRT. A theory of gravitation that allows non-symmetric energy-momentum tensors with non-vanishing divergence and that also has a geometric quantity to that the spin can couple directly is needed. This means one should use a generalization of GRT which makes only the necessary generalizations needed for constitutive theory. wwwitp.physik.tu-berlin.de /~hh/ALT/Dissertation/node18.html   (244 words)

Einstein-Cartan Theory Furthermore, Einstein-Cartan theory differs from the theory of general relativity only in that intrinsic angular momentum creates a torsion effect on the path of the body in question. The mathematical space that the theory of general relativity manipulates is a Riemannian spacetime. Using this theory, one can calculate the motions of planets within the solar system with an accuracy of 10^(-4). www.mrao.cam.ac.uk /~rh316/Research/einsteincartantheory.html   (181 words)

Cartan connection applications - TheBestLinks.com - Tetrad, General relativity, Isomorphism, Linear map, ... In any dimension, for a pseudo Riemannian geometry (with metric signature (p,q)), this Cartan connection theory is an alternative method in differential geometry. The vierbein or tetrad theory is the special case of a four-dimensional manifold. Since what we now have here is a SO(p,q) gauge theory, the Riemann curvature F defined as $\backslash bold\{F\}\backslash equiv\; d\backslash bold\{A\}+\backslash bold\{A\}\backslash wedge\backslash bold\{A\}$ is\; pointwise\; gauge\; covariant.$$ www.thebestlinks.com /Tetrad.html   (525 words)

VANISHING VIERBEIN The dynamical variables of a generalized Einstein-Cartan theory are: a principal connection By a pure gauge theory we mean a gauge field theory where the primitive fields have no direct connection to space-time geometry. 3 we formulate a gauge theory of the Lorentz group and point out that the requirement of smoothness of the Lagrangian at a degenerate vierbein is a strong selection criterion. quantumfuture.net /quantum_future/papers/vv   (1917 words)

Cartan's Corner (using Charlotte Technology) The theory is developed in terms of vectors and matrices of exterior differential forms, which permit the topological coherent structures of fields and particles that make up a "Physical Vacuum", as well as their topological fluctuations, to be readily evaluated in terms of a more or less "universal" theory. Cartan's methods of exterior differential forms are applied to a variety of physical problems. The eigenvectors of the 2-form are either vectors of eigenvalue zero, or isotropic complex Spinors (E. Cartan) of imaginary eigenvalues. www22.pair.com /csdc/car/carhomep.htm   (1160 words)

Introduction This would naturally introduce torsion into the geometry [4, 5, 6, 7], thus extending Riemann spacetime of the Einstein theory to Riemann-Cartan spacetime. Einstein's theory of general relativity predicts correctly all post-Newtonian experiments in our solar system as well as some effects of strong gravitational fields observed in binary systems of neutron stars [1]. So far, such spacetimes have only found applications in the theory of plastic flow and material fatigue [7, 8, 9, 10], where curvature and torsion are produced by disclinations and dislocations. www.physik.fu-berlin.de /~kleinert/kleiner_re262/node1.html   (659 words)

Torsion: Experimental investigation of new long-range actions. E.Cartan performed the first theoretical works devoted to a theory of gravitation containing torsion, but at the early stages, Cartan's gravitation theory never obtained support, since spin was not yet discovered at that time. Cartan was the first to point to the possibility of the existence of fields generated by the spin angular momentum density. In the framework of the theory of electro-torsion interactions [66], it is shown that if an electrostatic or electromagnetic field exists in some region of space, then there always exists a torsion field in that region of space. www.amasci.com /freenrg/tors/doc17.html   (5592 words)

Gravitation 2 Chern-Simons gravity in D=3 GR as a CS theory. Conservation laws - EC theory Asymptotic structure of spacetime. www.phy.bg.ac.yu /~mb/pg/gr2.html   (52 words)

posters.htm Realistic gravitational theories where the ground state of the theory has exactly zero energy density, without fine tuning parameters in the Lagrangian can be constructed using actions of the form $S =\int d^{D}x \Phi L_{1} + \int d^{D}x \sqrt{-g} L_{2} $, where $L_{1}$ and $L_{2}$ are both independent of the measure fields $\varphi_{j}$. As a previous step to introduce our metodology, we study the quantum theory of fields in Minkowski spacetime in the Bohm-de Broglie interpretation and exhibit a concrete example where Lorentz invariance of individual events is broken. field theory with torsion, through studying the Dirac equation in Weitzenbock spacetime, we obtain the evolutionary equation of the neutrino oscillation in vacuum. www.mat.unb.br /eventos/pirenopolis/posters.htm   (6929 words)

Cabi's Glasses: Mannheim's Conformal Gravity Another interesting property is G appears not in the fundamental theory but as an effective coupling constant. Idea is to write a fully conformal but generally covariant theory without introducing any new structure (like a gauge field as Weyl did or torsion). This is a pure metric theory, there is no extra structure. www.mit.edu /people/cabi/blog/2005/02/mannheims-conformal-gravity.html   (627 words)

Cartan curvature tensor Cartan's Corner : Torsion of Translation vs. Torsion of Expansion-Rotation... Geometric and analytic problems related to Cartan connections... D 12, 3013 (1975): Sandberg - Are torsion theories of...... www.scienceoxygen.com /phys/192.html   (117 words)

Topology and Physics Like Einstein's Gravitational Curvature of SpaceTime, the Gravitational Torsion of SpaceTime is an Effective Deformation of 4-dim Physical SpaceTime in which 4-dim Physical SpaceTime effectively appears to be, not an immutable RP1 x S3, but a Compressible Aether. In the theory of general relativity, the connection is provided by an object calledthe Christoffel symbol G_ij^k. As Cartan discovered, there are three canonical connections on a Lie group manifold. www.valdostamuseum.org /hamsmith/topolophys.html   (2894 words)

MATTER and SPACE with TORSION Note, that general relativity equations, equations of the Einstein-Cartan theory of gravitation with torsion [2, 5-6, 9-10, 15-16], and equations of different non-symmetric topological gravitational theories [11-12, 14] are dual. Following Clifford, Cartan, Einstein, Wheeler, Ivanenko, and others, we assume that this unified field is none other than curved space-time with torsion [1-7]. Einstein in [2] asserted that more complex Lagrangians should be analyzed only if there exist some physical causes based on experimental data. www.acadjournal.com /2003/v9/part4/p1   (4231 words)

Citebase - Complex Relativity: Gravity and Electromagnetic Fields , On manifolds with an affine connection and the theory of general relativity, Napoli:Bibliopolis, 1986. [34] R. Teisseyre, J. Suchcicki, K. Teisseyre, J. Wiszniowski, and P. Palangio, Seismic rotation waves:basic elements of the theory and recordings, Annals of Geophysics 46 (2003), 671-685. [20], Non-Riemannian geometrical approach to deformation and friction, Theory of Earthquake Premonitory and Fracture Processes (R. Teisseyre, ed.), PWN (Polish Scientic Publishers), Warszawa, 1995, pp. www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:physics/0506033   (812 words)

papers The MAG represents a gauge theoretical formulation of a theory of gravity which, in contrast to the theory of General Relativity (GR), is no longer confined to a pseudo-Riemannian spacetime structure. Within this theory there are new geometrical quantities, namely torsion and nonmetricity that act as additional field strengths similarly to the curvature in the general relativistic case. This thesis is concerned with the search for exact solutions in metric-affine gauge theory of gravity (MAG). www.thp.uni-koeln.de /~dp/papers.html   (2496 words)

Quadratic Lagrangians in Einstein-Cartan theory Two major figures in this are Élie Cartan and Dennis Sciama. www.mrao.cam.ac.uk /~rh316/Research/summary.html   (42 words)

G. David Kerlick Publications The Effect of Intrinsic Spin on Neutron Stars in the Einstein-Cartan Theory of Gravity, Astrophys. General Relativity with Spin and Torsion and its Deviation from Einstein's Theory -- with F.W. Hehl and P. v.d. Cartan, Élie, On a Generalization of the notion of Riemann curvature and spaces with torsion.(English) Translated from the French by G.D. Kerlick. www.eskimo.com /~davidk/prof/pubs.html   (1015 words)

Astro-ph for busy people From this the Einstein static universe with constant torsion is constructed, generalising the Einstein Cosmos to Einstein-Cartan theory. In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. To this end the post-Newtonian expansion of the Einstein and light geodesic equations in the case of a gravitating system comprised of N massive bodies is employed. www.camk.edu.pl /~gwar/astro-ph/2003.10.14.html   (6807 words)

Topology and Physics A complete geometric unification of gravity and electromagnetism is proposed by considering two aspects of torsion: its relation to spin established in Einstein-Cartan theory and the possible interpretation of the torsion trace as the electromagnetic potential. the theory is formally similar in its equations (hence local behaviour) to the Einstein-Cartan-Kibble-Sciama spin-torsion theory, but it restricts the Lagrangian type and the torsion type (... For this reason, the long-standing relation between the torsion trace and the electromagnetic potential is merely a formal consequence of the geometrical background underlying the new theory. www.valdostamuseum.org /hamsmith/topolophys2.html   (3793 words)

Jerry Griffiths - Publications A contribution to the Rainich theory of the neutrino field. A contribution to the Rainich theory of the neutrino field II. The application of spin coefficient techniques in the vacuum quadratic Poincaré gauge field theory. www-staff.lboro.ac.uk /~majbg/jbg/JBGpapers.html   (463 words)

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