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Yakov Itin - One of the best experts on this subject based on the ideXlab platform.
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Coframe teleparallel models of gravity. Exact solutions.”, gr-qc/9912013
2013Co-Authors: Yakov ItinAbstract:The superstring and superbrane theories include gravity as a necessary and fundamental part of a (future) unified field theory. Thus it is important to consider the alternative representations of general relativity as well as the alternative models of gravity. We study the Coframe teleparallel theory of gravity with a most general quadratic Lagrangian. The Coframe field on a differentiable manifold is a basic dynamical variable. A metric tensor as well as a metric compatible connection is generated by a Coframe in a unique manner. The Lagrangian is a general linear combination of Weitzenböck’s quadratic invariants with free dimensionless parameters ρ1, ρ2, ρ3. Every independent term of the Lagrangian is a global SO(1, 3)-invariant 4-form. For a special choice of parameters which confirms with the local SO(1, 3) invariance this theory gives an alternative description of Einsteinian gravity- teleparallel equivalent of GR. The field equations of the theory is studied by a “diagonal ” Coframe ansatz which is a subclass of a most general spherical-symmetric Einstein-Mayer ansatz. The restricted Lagrangian depends only on two free parameters ρ1, ρ3. We obtain a formula for scalar curvature of a pseudo-Riemannian manifold with a metric constructed from the static “diagonal ” solution of the field equation. It is proved that the sign of the scalar curvature depends only on a relation between the parameters ρ1 and ρ3. Thus by a specific choice of free parameters a manifold of positive or negative curvature can be obtained. The scalar curvature vanishes only for a subclass of models with ρ1 = 0. This subclass includes the teleparallel equivalent of GR. We obtain the explicit form of all spherically symmetric static solutions of the “diagonal” type to the field equations for an arbitrary choice of free parameters. We prove that the unique asymptotic-flat solution with Newtonian limit is the Schwarzschild solution that holds for a subclass of teleparallel models with ρ1 = 0. Thus the Yang-Mills-type term of the general quadratic Coframe Lagrangian should be rejected
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Coframe energy-momentum current. Algebraic properties, Gen. Rel. Grav. 34 (2002) 1819-1837; arXiv:gr-qc/0111087. Copyright line will be provided by the publisher header will be provided by the publisher 13
2013Co-Authors: Yakov ItinAbstract:Abstract. The Coframe (teleparallel) description of gravity is known as a viable alternative to GR. One of advantages of this model is the existence of a conserved energy-momentum current witch is covariant under all symmetries of the threeparameter Lagrangian. In this paper we study the relation between the covector valued current and the energy-momentum tensor. Algebraic properties of the conserved current for different values of parameters are derived. It is shown that the tensor corresponding to the Coframe current is traceless and, in contrast to the electromagnetic field, has in general a non vanishing antisymmetric part. The symmetric part is also non zero for all values of the parameters. Consequently, the conserved current involves the energy-momentum as well as the rotational (spin) properties of the field
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Coframe geometry, gravity and electromagnetism
Journal of Physics: Conference Series, 2013Co-Authors: Yakov ItinAbstract:The extensions of GR for description of fermions on a curved space, for supergravity, and for the loop quantum gravity ordinary use a set of 16 independent variables instead of 10 components of metric. These variables can be assembled in a Coframe field, i.e., a set of four linearly independent 1-forms. In this presentation we review a geometrical structure based on the Coframe field. We construct a complete class of the Coframe connections which are linear in the first order derivatives of the Coframe field on an n dimensional manifolds with and without a metric. The subclasses of the torsion-free, metric-compatible and flat connections are derived. We also study the behavior of the geometrical structures under local transformations of the Coframe. The remarkable fact is an existence of a subclass of connections which are invariant when the infinitesimal transformations satisfy the Maxwell-like system of equations.
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Coframe geometry and gravity
arXiv: General Relativity and Quantum Cosmology, 2007Co-Authors: Yakov ItinAbstract:The possible extensions of GR for description of fermions on a curved space, for supergravity and for loop quantum gravity require a richer set of 16 independent variables. These variables can be assembled in a Coframe field, i.e., a local set of four linearly independent 1-forms. In the ordinary formulation, the Coframe gravity does not have any connection to a specific geometry even being constructed from the geometrical meaningful objects. A geometrization of the Coframe gravity is an aim of this paper. We construct a complete class of the Coframe connections which are linear in the first order derivatives of the Coframe field on an $n$ dimensional manifolds with and without a metric. The subclasses of the torsion-free, metric-compatible and flat connections are derived. We also study the behavior of the geometrical structures under local transformations of the Coframe. The remarkable fact is an existence of a subclass of connections which are invariant when the infinitesimal transformations satisfy the Maxwell-like system of equations. In the framework of the Coframe geometry construction, we propose a geometrical action for the Coframe gravity. It is similar to the Einstein-Hilbert action of GR, but the scalar curvature is constructed from the general Coframe connection. We show that this geometric Lagrangian is equivalent to the Coframe Lagrangian up to a total derivative term. Moreover there is a family of Coframe connections which Lagrangian does not include the higher order terms at all. In this case, the equivalence is complete.
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Maxwell-type behaviour from a geometrical structure
Classical and Quantum Gravity, 2006Co-Authors: Yakov ItinAbstract:We study which geometric structure can be constructed from the vierbein (frame/Coframe) variables and which field models can be related to this geometry. The Coframe field models, alternative to GR, are known as viable models for gravity, since they have the Schwarzschild solution. Since the local Lorentz invariance is violated, a physical interpretation of additional six degrees of freedom is required. The geometry of such models is usually given by two different connections—the Levi-Civita symmetric and metric-compatible connection and the Weitzenbock flat connection. We construct a general family of linear connections of the same type, which includes two connections above as special limiting cases. We show that for dynamical propagation of six additional degrees of freedom it is necessary for the gauge field of infinitesimal transformations (antisymmetric tensor) to satisfy the system of two first-order differential equations. This system is similar to the vacuum Maxwell system and even coincides with it on a flat manifold. The corresponding 'Maxwell-compatible connections' are derived. Alternatively, we derive the same Maxwell-type system as a symmetry condition of the viable model Lagrangian. Consequently, we derive a nontrivial decomposition of the Coframe field to the pure metric field plus a dynamical field of infinitesimal Lorentz rotations. An exact spherical-symmetric solution for our dynamical field is derived. It is bounded near the Schwarzschild radius. Further off, the solution is close to the Coulomb field.
Friedrich W. Hehl - One of the best experts on this subject based on the ideXlab platform.
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Quantum gravity model with fundamental spinor fields
Physics of Particles and Nuclei, 2014Co-Authors: Yuri N. Obukhov, Friedrich W. HehlAbstract:We discuss the possibility that gravitational potentials (metric, Coframe and connection) may emerge as composite fields from more fundamental spinor constituents. We use the formalism of Poincare gauge gravity as an appropriate theoretical scheme for the rigorous development of such an approach. We postulate the constitutive relations of an elastic Cosserat type continuum that models spacetime. These generalized Hooke and MacCullagh type laws consistently take into account the translational and Lorentz rotational deformations, respectively. The resulting theory extends the recently proposed Diakonov model. An intriguing feature of our theory is that in the lowest approximation it reproduces Heisenberg’s nonlinear spinor model.
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An assessment of Evans’ unified field theory
2013Co-Authors: Friedrich W. HehlAbstract:Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal Coframe ϑ α and a (metric compatible) Lorentz connection Γ αβ. These two potentials yield the field strengths torsion T α and curvature R αβ. Evans tried to infuse electromagnetic properties into this geometrical framework by putting the Coframe ϑ α to be proportional to four extended electromagnetic potentials A α; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan(-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans ’ ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete
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Extended Einstein–Cartan theory à la Diakonov: The field equations
Physics Letters B, 2012Co-Authors: Yuri N. Obukhov, Friedrich W. HehlAbstract:Abstract Diakonov formulated a model of a primordial Dirac spinor field interacting gravitationally within the geometric framework of the Poincare gauge theory (PGT). Thus, the gravitational field variables are the orthonormal Coframe (tetrad) and the Lorentz connection. A simple gravitational gauge Lagrangian is the Einstein–Cartan choice proportional to the curvature scalar plus a cosmological term. In Diakonovʼs model the Coframe is eliminated by expressing it in terms of the primordial spinor. We derive the corresponding field equations for the first time. We extend the Diakonov model by additionally eliminating the Lorentz connection , but keeping local Lorentz covariance intact. Then, if we drop the Einstein–Cartan term in the Lagrangian, a nonlinear Heisenberg type spinor equation is recovered in the lowest approximation.
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Extended Einstein-Cartan theoryla Diakonov: the field equations
2012Co-Authors: Yuri N. Obukhov, Friedrich W. HehlAbstract:Diakonov formulated a model of a primordial Dirac spinor field interact- ing gravitationally within the geometric framework of the Poincare gauge theory (PGT). Thus, the gravitational field variables are the orthonormal Coframe (tetrad) and the Lorentz connection. A simple gravitational gauge Lagrangian is the Einstein-Cartan choice proportional to the curvature scalar plus a cosmological term. In Diakonov's model the Coframe is eliminated by expressing it in terms of the primordial spinor. We derive the correspond- ing field equations for the first time. We extend the Diakonov model by additionally eliminating the Lorentz connection, but keeping local Lorentz covariance intact. Then, if we drop the Einstein-Cartan term in the La- grangian, a nonlinear Heisenberg type spinor equation is recovered in the lowest approximation.
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An Assessment of Evans’ Unified Field Theory I
Foundations of Physics, 2007Co-Authors: Friedrich W. HehlAbstract:Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal Coframe ϑ ^ α and a (metric compatible) Lorentz connection Γ ^ α β . These two potentials yield the field strengths torsion T ^ α and curvature R ^ α β . Evans tried to infuse electromagnetic properties into this geometrical framework by putting the Coframe ϑ ^ α to be proportional to four extended electromagnetic potentials $\mathcal{A}^{\alpha }$ ; these are assumed to encompass the conventional Maxwellian potential A in a suitable limit. The viable Einstein-Cartan (-Sciama-Kibble) theory of gravity was adopted by Evans to describe the gravitational sector of his theory. Including also the results of an accompanying paper by Obukhov and the author, we show that Evans’ ansatz for electromagnetism is untenable beyond repair both from a geometrical as well as from a physical point of view. As a consequence, his unified theory is obsolete.
D Vassiliev - One of the best experts on this subject based on the ideXlab platform.
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Modelling the neutrino in terms of Cosserat elasticity
The Twelfth Marcel Grossmann Meeting, 2012Co-Authors: Olga Chervova, D VassilievAbstract:The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the the spinor field oscillates har- monically in time. We suggest a new geometric interpretation of the stationary Weyl equation, one which does not require the use of spinors, Pauli matrices or covariant dif- ferentiation. We think of our 3-dimensional space as an elastic continuum and assume that material points of this continuum can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of ma- Terial points of the space continuum are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the Coframe. As the dynamical variables (unknowns) of our theory we choose the Coframe and a density. We choose a particular potential energy which is conformally invariant and then incorporate time into our action in the standard Newtonian way, by subtracting kinetic energy. The main result of our paper is the theorem stating that in the stationary setting our model is equivalent to a pair of Weyl equations. The crucial element of the proof is the observation that our Lagrangian admits a factorisation. Copyright © 2012 by World Scientific Publishing Co. Pte. Ltd.
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The stationary Weyl equation and Cosserat elasticity
Journal of Physics A: Mathematical and Theoretical, 2010Co-Authors: Olga Chervova, D VassilievAbstract:The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of the stationary Weyl equation. We think of our three-dimensional space as an elastic continuum and assume that material points of this continuum can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. The rotations of material points of the space continuum are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the Coframe. As the dynamical variables (unknowns) of our theory, we choose the Coframe and a density. We choose a particular potential energy which is conformally invariant and then incorporate time into our action in the standard Newtonian way, by subtracting kinetic energy. The main result of our paper is the theorem stating that in the stationary setting our model is equivalent to a pair of Weyl equations.
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Modelling the neutrino in terms of Cosserat elasticity
arXiv: Mathematical Physics, 2010Co-Authors: Olga Chervova, D VassilievAbstract:The paper deals with the Weyl equation which is the massless Dirac equation. We study the Weyl equation in the stationary setting, i.e. when the the spinor field oscillates harmonically in time. We suggest a new geometric interpretation of the stationary Weyl equation, one which does not require the use of spinors, Pauli matrices or covariant differentiation. We think of our 3-dimensional space as an elastic continuum and assume that material points of this continuum can experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points of the space continuum are described mathematically by attaching to each geometric point an orthonormal basis which gives a field of orthonormal bases called the Coframe. As the dynamical variables (unknowns) of our theory we choose the Coframe and a density. We choose a particular potential energy which is conformally invariant and then incorporate time into our action in the standard Newtonian way, by subtracting kinetic energy. The main result of our paper is the theorem stating that in the stationary setting our model is equivalent to a pair of Weyl equations. The crucial element of the proof is the observation that our Lagrangian admits a factorisation.
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Massless Dirac equation as a special case of Cosserat elasticity
Journal of the Association of Arab Universities for Basic and Applied Sciences, 2009, vol. 7, p. 25-42. (Proceedings of the International Conference o, 2009Co-Authors: D VassilievAbstract:We suggest an alternative mathematical model for the massless neutrino. Consider an elastic continuum in 3-dimensional Euclidean space and assume that points of this continuum can experience no displacements, only rotations. This framework is a special case of the so-called Cosserat theory of elasticity. Rotations of points of the continuum are described by attaching to each point an orthonormal basis which gives a field of orthonormal bases called the Coframe. As the dynamical variables (unknowns) of our theory we choose a Coframe and a density. We write down a potential energy which is conformally invariant and then incorporate time in the standard Newtonian way, by subtracting kinetic energy. Finally, we rewrite the resulting nonlinear variational problem in terms of an unknown spinor field. We look for quasi-stationary solutions, i.e. solutions that harmonically oscillate in time. We prove that in the quasi-stationary setting our model is equivalent to a pair of massless Dirac equations. The crucial element of the proof is the observation that our Lagrangian admits a factorisation.
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Weyl's Lagrangian in teleparallel form
Journal of Mathematical Physics, 2009Co-Authors: James Burnett, D VassilievAbstract:The Weyl Lagrangian is the massless Dirac Lagrangian. The dynamical variable in the Weyl Lagrangian is a spinor field. We provide a mathematically equivalent representation in terms of a different dynamical variable — the Coframe (an orthonormal tetrad of covector fields). We show that when written in terms of this dynamical variable, the Weyl Lagrangian becomes remarkably simple: it is the wedge product of axial torsion of the teleparallel connection with a teleparallel lightlike element of the Coframe. We also examine the issues of U(1)-invariance and conformal invariance. Examination of the latter motivates us to introduce a positive scalar field (equivalent to a density) as an additional dynamical variable; this makes conformal invariance self-evident.
Meilin Shi - One of the best experts on this subject based on the ideXlab platform.
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Coframe a framework for cscw applications based on grid and web services
International Conference on Web Services, 2005Co-Authors: Jinlei Jiang, Shaohua Zhang, Meilin ShiAbstract:Though 20 years have passed since the birth of CSCW, the original goal of it is not reached as well as people expected. This situation is mostly due to the supporting technology especially the infrastructure. Today, great changes have taken place in technology, including grid computing and Web services. These technologies, we think, significantly affect the application of CSCW. In this paper, a framework called Coframe is proposed to answer the challenges faced by CSCW. Based on the emerging grid and Web service technologies, Coframe provides some general yet flexible cooperation related services and organizes them into different layers. The elaborately designed services and architecture make Coframe adaptive to diverse requirements of different domains. The paper details the framework and demonstrates its application with a case study in e-learning.
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ICWS - Coframe: a framework for CSCW applications based on grid and Web services
IEEE International Conference on Web Services (ICWS'05), 2005Co-Authors: Jinlei Jiang, Shaohua Zhang, Meilin ShiAbstract:Though 20 years have passed since the birth of CSCW, the original goal of it is not reached as well as people expected. This situation is mostly due to the supporting technology especially the infrastructure. Today, great changes have taken place in technology, including grid computing and Web services. These technologies, we think, significantly affect the application of CSCW. In this paper, a framework called Coframe is proposed to answer the challenges faced by CSCW. Based on the emerging grid and Web service technologies, Coframe provides some general yet flexible cooperation related services and organizes them into different layers. The elaborately designed services and architecture make Coframe adaptive to diverse requirements of different domains. The paper details the framework and demonstrates its application with a case study in e-learning.
Jinlei Jiang - One of the best experts on this subject based on the ideXlab platform.
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Coframe a framework for cscw applications based on grid and web services
International Conference on Web Services, 2005Co-Authors: Jinlei Jiang, Shaohua Zhang, Meilin ShiAbstract:Though 20 years have passed since the birth of CSCW, the original goal of it is not reached as well as people expected. This situation is mostly due to the supporting technology especially the infrastructure. Today, great changes have taken place in technology, including grid computing and Web services. These technologies, we think, significantly affect the application of CSCW. In this paper, a framework called Coframe is proposed to answer the challenges faced by CSCW. Based on the emerging grid and Web service technologies, Coframe provides some general yet flexible cooperation related services and organizes them into different layers. The elaborately designed services and architecture make Coframe adaptive to diverse requirements of different domains. The paper details the framework and demonstrates its application with a case study in e-learning.
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ICWS - Coframe: a framework for CSCW applications based on grid and Web services
IEEE International Conference on Web Services (ICWS'05), 2005Co-Authors: Jinlei Jiang, Shaohua Zhang, Meilin ShiAbstract:Though 20 years have passed since the birth of CSCW, the original goal of it is not reached as well as people expected. This situation is mostly due to the supporting technology especially the infrastructure. Today, great changes have taken place in technology, including grid computing and Web services. These technologies, we think, significantly affect the application of CSCW. In this paper, a framework called Coframe is proposed to answer the challenges faced by CSCW. Based on the emerging grid and Web service technologies, Coframe provides some general yet flexible cooperation related services and organizes them into different layers. The elaborately designed services and architecture make Coframe adaptive to diverse requirements of different domains. The paper details the framework and demonstrates its application with a case study in e-learning.