Emerging gravity from defects in world crystal

Kleinert, H.

doi:10.1590/s0103-97332005000200022

Cited by 11 publications

(6 citation statements)

References 11 publications

(7 reference statements)

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“…Notwithstanding that such crystals are, of course, not to be found in standard condensed matter, higher dimensional glide constraints might have implications for 'emergence theories' of fundamental phenomena resting on elasticity theory 52,60 . Let us for example look how the constraint Eq.…”

Section: The Electrically Charged Medium and Glidementioning

confidence: 99%

“…Having a mathematical definition of the glide constraint at our fingertips enables us to address its incarnations in even higher dimensional systems where direct visualization is of little use. Notwithstanding that such crystals are, of course, not to be found in standard condensed matter, higher dimensional glide constraints might have implications for 'emergence theories' of fundamental phenomena resting on elasticity theory 52,60 . Let us for example look how the constraint Eq.…”

Section: The Electrically Charged Medium and Glidementioning

confidence: 99%

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Topological kinematic constraints: dislocations and the glide principle

Cvetković

Nussinov

Zaanen

2006

Philosophical Magazine

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Topological defects play an important role in physics of elastic media and liquid crystals. Their kinematics is determined by constraints of topological origin. An example is the glide motion of dislocations which has been extensively studied by metallurgists. In a recent theoretical study dealing with quantum dualities associated with the quantum melting of solids it was argued that these kinematic constraints play a central role in defining the quantum field theories of relevance to the description of quantum liquid crystalline states of the nematic type. This forms the motivation to analyze more thoroughly the climb constraints underlying the glide motions. In the setting of continuum field theory the climb constraint is equivalent to the condition that the density of constituent particles is vanishing and we derive a mathematical definition of this constraint which has a universal status. This makes possible to study the kinematics of dislocations in arbitrary space-time dimensions and as an example we analyze the restricted climb associated with edge dislocations in 3+1D. Very generally, it can be shown that the climb constraint is equivalent to the condition that dislocations do not communicate with compressional stresses at long distances. However, the formalism makes possible to address the full non-linear theory of relevance to short distance behaviors where violations of the constraint become possible.

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Section: The Electrically Charged Medium and Glidementioning

confidence: 99%

Section: The Electrically Charged Medium and Glidementioning

confidence: 99%

Topological kinematic constraints: dislocations and the glide principle

Cvetković

Nussinov

Zaanen

2006

Philosophical Magazine

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“…Kleinert [36][37][38][39] used a linear perturbation of the coordinate frame by a displacement field generating strain and consequently revealed that space-time with torsion and curvature can be generated from a flat Euclidean space-time using singular coordinate transformations. He argued in favor of comparing the above to a crystallographic medium filled with dislocations and disclinations.…”

Section: Physical Interpretation Of the Spectral Normsmentioning

confidence: 99%

“…Recall that the spectral norm of a transformation matrix reflects the largest singular value of the matrix that entails the maximum extent of allowable deformation (stretching) of vectors in the corresponding vector space [54]. Kleinert [55,56,57,58] used a linear perturbation of the coordinate frame by a displacement field generating strain, and consequently revealed that space-time with torsion and curvature can be generated from a flat Euclidean space-time using singular coordinate transformations. He argued in favor of comparing the above to a crystallographic medium filled with dislocations and disclinations.…”

Section: Physical Interpretation Of the Spectral Normsmentioning

confidence: 99%

Emergence of an Aperiodic Dirichlet Space from the Tetrahedral Units of an Icosahedral Internal Space

Sen¹,

Aschheim²,

Irwin³

2017

Mathematics

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Abstract:We present the emergence of a root system in six dimensions from the tetrahedra of an icosahedral core known as the 20-group (20G) within the framework of Clifford's geometric algebra. Consequently, we establish a connection between a three-dimensional icosahedral seed, a six-dimensional (6D) Dirichlet quantized host and a higher dimensional lattice structure. The 20G, owing to its icosahedral symmetry, bears the signature of a 6D lattice that manifests in the Dirichlet integer representation. We present an interpretation whereby the three-dimensional 20G can be regarded as the core substratum from which the higher dimensional lattices emerge. This emergent geometry is based on an induction principle supported by the Clifford multi-vector formalism of three-dimensional (3D) Euclidean space. This lays a geometric framework for understanding several physics theories related to SU(5), E 6 , E 8 Lie algebras and their composition with the algebra associated with the even unimodular lattice in R 3,1 . The construction presented here is inspired by Penrose's three world model.

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“…In [14] it is shown that a spacetime with curvature and torsion can be considered as a state of a four-dimensional continuum containing defects, in analogy with the CMP continuous theory of [4]. In [15] it is claimed that gravitation stems from a distribution of continuous defects. Let us first give a short reminder of the theory of defects (for a detailed overview see [16]):…”

Section: Introductionmentioning

confidence: 99%

Some Aspects of Defect Theory in Spacetime

Kléman

2015

The Thirteenth Marcel Grossmann Meeting

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The topological theory and the Volterra process are key tools for the classification of defects in Condensed Mater Physics. We employ the same methods to classify the 2D defects of a 4D maximally symmetric spacetime. These cosmic forms, which are continuous, fall into three classes: i)m-forms, akin to 3D space disclinations, analogous to Kibble's cosmic strings; ii)t-forms, related to hyperbolic rotations; iii)r-forms, never considered so far, related to null rotations. A detailed account of their metrics is presented. There are wedge forms, whose singularities occupy a 2D world sheet, and twist forms, whose singularities occupy a 3D world shell. m-forms are compatible with the cosmological principle of space homogeneity and isotropy, t-and r-forms demand spacetime homogeneity. t-and r-forms are typical of a vacuum obeying the perfect cosmological principle in a de Sitter spacetime. Cosmic forms may assemble into networks generating vanishing curvature.

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Emerging gravity from defects in world crystal

Cited by 11 publications

References 11 publications

Topological kinematic constraints: dislocations and the glide principle

Topological kinematic constraints: dislocations and the glide principle

Emergence of an Aperiodic Dirichlet Space from the Tetrahedral Units of an Icosahedral Internal Space

Some Aspects of Defect Theory in Spacetime

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