Unification Principle and a Geometric Field Theory

Wanas, M. I.; Osman, Samah N.; El-Kholy, Reham I.

doi:10.1515/phys-2015-0030

Cited by 11 publications

(9 citation statements)

References 35 publications

(45 reference statements)

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“…It has been applied successfully in the context of conventional APgeometry (cf. [13,28,34]), using the differential identity (1.3).…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…The later depends on the choice of the Lagrangian density L which has many forms in AP-geometry. Several field theories have been constructed [13,28,34], using the geometrization philosophy and the identity (1.3). Many successful applications have been obtained within these theories [2,3,9,14,21,25,29].…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown that many other scalars can be defined in AP-geometry and its different versions. These scalars have been used to construct several field theories with GR limits [13,28,30,34,35,36].…”

Section: Introductionmentioning

confidence: 99%

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Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

Wanas

Youssef

Hanafy

et al. 2016

Advances in Mathematical Physics

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The importance of Einstein's geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified. The use of Bianchi identity to write the field equations of GR is shown. Another similar identity in the absolute parallelism geometry is given. A more general differential identity in the parameterized absolute parallelism geometry is derived. Comparison and interrelationships between the above mentioned identities and their role in constructing field theories are discussed.

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“…It has been applied successfully in the context of conventional APgeometry (cf. [13,28,34]), using the differential identity (1.3).…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

Wanas

Youssef

Hanafy

et al. 2016

Advances in Mathematical Physics

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“…It is worth to see different approaches to study gravity by examining connections other than Weitzenböck [51][52][53][54][55][56][57][58], which may have an interesting astrophysical and cosmological applications [59][60][61][62]. One can show that equation (6) implies the metricity condition.…”

Section: A Installing Weitzenböck Connectionmentioning

confidence: 99%

Reconstruction of f ( T ) $f(T)$ -gravity in the absence of matter

Hanafy¹,

Nashed²

2016

Astrophys Space Sci

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We derive an exact f (T ) gravity in the absence of ordinary matter in Friedmann-RobertsonWalker (FRW) universe, where T is the teleparallel torsion scalar. We show that vanishing of the energy-momentum tensor T µν of matter does not imply vanishing of the teleparallel torsion scalar, in contrast to general relativity, where the Ricci scalar vanishes. The theory provides an exponential (inflationary) scale factor independent of the choice of the sectional curvature. In addition, the obtained f (T ) acts just like cosmological constant in the flat space model. Nevertheless, it is dynamical in non-flat models. In particular, the open universe provides a decaying pattern of the f (T ) contributing directly to solve the fine-tuning problem of the cosmological constant. The equation of state (EoS) of the torsion vacuum fluid has been studied in positive and negative Hubble regimes. We study the case when the torsion is made of a scalar field (tlaplon) which acts as torsion potential. This treatment enables to induce a tlaplon field sensitive to the symmetry of the spacetime in addition to the reconstruction of its effective potential from the f (T ) theory. The theory provides six different versions of inflationary models. The real solutions are mainly quadratic, the complex solutions, remarkably, provide Higgs-like potential.PACS numbers: 98.80.Qc, 04.20.Cv, 98.80.Cq.

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“…Similarly, the W-tensor of the type given by (56-60) cannot be defined in other geometry, but the Ap-geometry and its different versions. This tensor is important in constructing field theories [15], [16]. Many Ap-structures have been constructed for different applications cf.…”

mentioning

confidence: 99%

An AP structure with Finslerian Flavor: Path equations

2016

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The Bazanski approach for deriving paths is applied to Finsler geometry. The approach is generalized and applied to a new developed geometry called "Absolute parallelism with a Finslerian Flavor" (FAP). A sets of path equations is derived for the FAP. This is the horizontal (h) set. A striking feature appears in this set, that is: the coefficient of torsion term, in the set, jumps by a step of one-half from one equation to the other. This is tempting to believe that the h-set admits some quantum features. Comparisons with the corresponding sets in other geometries are given. Conditions to reduce the set of path equations obtained, to well known path equations in some geometries are summarized in a schematic diagram.

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Unification Principle and a Geometric Field Theory

Cited by 11 publications

References 35 publications

Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

Reconstruction of f ( T ) $f(T)$ -gravity in the absence of matter

An AP structure with Finslerian Flavor: Path equations

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