Cylindrical Geometric Defects and Multi-Wall Nanotubes

Berredo-Peixoto, Guilherme de; Katanaev, M. O.; Konstantinova, Elena V.; Shapiro, I. L.

doi:10.1142/9789814623995_0491

Cited by 3 publications

(3 citation statements)

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“…here (7) is of no consequence, generating only a total derivative, if the theory is torsion free. However, in the presence of torsion this constant gets operative.…”

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confidence: 99%

Big Bounce and Inflation From Gravitational Four-Fermion Interaction

Khriplovich¹

2013

Low Dimensional Physics and Gauge Principles

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The four-fermion gravitational interaction is induced by torsion, and gets dominating on the Planck scale. The regular, axial-axial part of this interaction by itself does not stop the gravitational compression. However, the anomalous, vector-vector interaction results in a natural way both in big bounce and in inflation.Keywords: Planck scale; gravitational four-fermion interaction; big bounce; inflation.1. The observation that, in the presence of torsion, the interaction of fermions with gravity results in the four-fermion interaction of axial currents, goes back at least to Ref. 1.We start our discussion of the four-fermion gravitational interaction with the analysis of its most general form.As has been demonstrated in Ref. 2, the common action for the gravitational field can be generalized as follows:here and below G is the Newton gravitational constant, I, J = 0, 1, 2, 3 (and M, N below) are internal Lorentz indices, µ, ν = 0, 1, 2, 3 are space-time indices, e I µ is the tetrad field, e is its determinant, and e µ I is the object inverse to e I µ . The curvature tensor is

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“…here (7) is of no consequence, generating only a total derivative, if the theory is torsion free. However, in the presence of torsion this constant gets operative.…”

mentioning

confidence: 99%

Big Bounce and Inflation From Gravitational Four-Fermion Interaction

Khriplovich¹

2013

Low Dimensional Physics and Gauge Principles

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“…Therefore, when we construct based on NCG a gravity theory which possesses physically important property such as conformal invariance, renormalizability, if we want the theory able to be extended supersymmetrically, we should build its action not to include Ricci curvature tensor. For example, one of the simplest theory which possesses local conformal symmetry and renormalizabilty consists of the Weyl action term d 4 x √ −gC 2 and the Gauss-Bonnet topological term and surface terms d 4 x √ −g(ηG b + τ R) [17] , where C 2 and G b terms are given by…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Supergravity on the noncommutative geometry

Shimojo

Ishihara

Kataoka

et al. 2017

Progress of Theoretical and Experimental Physics

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Two years ago, we found the supersymmetric counterpart of the spectral triple which specified noncommutative geometry. Based on the triple, we derived gauge vector supermultiplets, Higgs supermultiplets of the minimum supersymmetric standard model and its action. However, unlike the famous theories of Connes and his co-workers, the action does not couple to gravity. In this paper, we obtain the supersymmetric Dirac operator D (SG) M on the Riemann-Cartan curved space replacing derivatives which appear in that of the triple with the covariant derivatives of general coordinate transformation. We apply the supersymmetric version of the spectral action principle and investigate the heat kernel expansion on the square of the Dirac operator. As a result, we obtain a new supergravity action which does not include the Ricci curvature tensor.

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“…This means that the curvature and torsion tensors, respectively, are interpreted as surface densities of Frank and Burgers vectors and thus linked to the nonlinear, generally inelastic deformations of a solid. Recently, the qualitatively new kind of geometric defect has been described in [6] (see also [7]), corresponding to a tube dislocation (with cylindrical symmetry).…”

Section: Introductionmentioning

confidence: 99%

Geodesics in a space with a spherically symmetric dislocation

Andrade

Berredo-Peixoto

2013

Gravit. Cosmol.

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We consider a new type of defect in the scope of linear elasticity theory, using geometrical methods. This defect is produced by a spherically symmetric dislocation, or ball dislocation. We derive the induced metric as well as the affine connections and curvature tensors. Since the induced metric is discontinuous, one can expect ambiguity coming from these quantities, due to products between delta functions or its derivatives, plaguing a description of ball dislocations based on the Geometric Theory of Defects. However, exactly as in the previous case of cylindric defect, one can obtain some well-defined physical predictions of the induced geometry. In particular, we explore some properties of test particle trajectories around the defect and show that these trajectories are curved but can not be circular orbits.

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Cylindrical Geometric Defects and Multi-Wall Nanotubes

Cited by 3 publications

References 0 publications

Big Bounce and Inflation From Gravitational Four-Fermion Interaction

Big Bounce and Inflation From Gravitational Four-Fermion Interaction

Supergravity on the noncommutative geometry

Geodesics in a space with a spherically symmetric dislocation

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