The unexpected resurgence of Weyl geometry in late 20-th century physics

Scholz, Erhard

doi:10.48550/arxiv.1703.03187

Cited by 28 publications

(44 citation statements)

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“…In the new perspective it emerges that classical Weyl geometry of space-time has not only a nontrivial topological structure it also admits statistical interpretation of geometric quantities. Appraisal of a comprehensive review on Weyl geometry [9] and a critical reading of Dirac's paper [10] show that most of the present work is a new contribution. The significance of our work lies in the fact that rather than discarding the reality of space and time we articulate a framework in which space and time constitute fundamental physical reality.…”

Section: Introductionmentioning

confidence: 88%

Weyl geometry, topology of space-time and reality of electromagnetic potentials, and new perspective on particle physics

Tiwari

2020

Preprint

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Consistency of Weyl natural gauge, Lorentz gauge and nonlinear gauge is studied in Weyl geometry. Field equations in generalized Weyl-Dirac theory show that spinless electron and photon are topological defects. Statistical metric and fluctuating metric in 3D space with time as a measure of spatial relations are discussed to propose a statistical interpretation of Maxwell field equations. It is argued that physical geometry is an approximation to mathematical geometry, and 4D relativistic spacetime is essentially 3D space with changing spatial relations. The present work is suggested to have radical new outlook on elementary particle physics.

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Section: Introductionmentioning

confidence: 88%

Weyl geometry, topology of space-time and reality of electromagnetic potentials, and new perspective on particle physics

Tiwari

2020

Preprint

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“…The connection in Weyl geometry is no longer metric compatible. Moreover, a new vector field, known as Weyl vector field, is introduced, allowing to write the Weyl connection as [52,53],…”

Section: A Quick Start For Weyl Geometrymentioning

confidence: 99%

“…In this case the Weyl geometry is called integrable, and the length of vectors will be unchanged under a parallel transport along closed paths. For a detailed discussion of Weyl geometry see [51][52][53].…”

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confidence: 99%

Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity

Yang,

Shahidi,

Harko

et al. 2021

Preprint

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We consider the geodesic deviation equation, describing the relative accelerations of nearby particles, and the Raychaudhuri equation, giving the evolution of the kinematical quantities associated with deformations (expansion, shear and rotation) in the Weyl-type f (Q, T ) gravity, in which the non-metricity Q is represented in the standard Weyl form, fully determined by the Weyl vector, while T represents the trace of the matter energy-momentum tensor. The effects of the Weyl geometry and of the extra force induced by the non-metricity-matter coupling are explicitly taken into account. The Newtonian limit of the theory is investigated, and the generalized Poisson equation, containing correction terms coming from the Weyl geometry, and from the geometry matter coupling, is derived. As a physical application of the geodesic deviation equation the modifications of the tidal forces, due to the non-metricity-matter coupling, are obtained in the weak-field approximation. The tidal motion of test particles is directly influenced by the gradients of the extra force, and of the Weyl vector. As a concrete astrophysical example we obtain the expression of the Roche limit (the orbital distance at which a satellite begins to be tidally torn apart by the body it orbits) in the Weyl-type f (Q, T ) gravity.

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“…There are many generalization to Einstein's theory of gravity [1][2][3][4][5][6][7][8], even though Scalar-Tensor Theory deserve a special consideration. Using extended version of Einstein's theory, namely the Scalar -Tensor theory of Gravity [9], it is found that the quantum theory can be incorporated into gravity in a geometric manner.…”

Section: Introductionmentioning

confidence: 99%

Geometrization of Scalar and Spinor Electrodynamics via Bohmian Quantum Gravity

Joseph

2018

Preprint

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Quantum theory is formulated as a probabilistic theory on a flat Minkowski space-time, while general theory of relativity is formulated on a curved manifold as a geometric theory. Bohmian Quantum Gravity approach indicates that one need to convert a probabilistic theory to a geometric form to merge it with general theory of relativity. We explore the differential geometric formulation of Scalar Electrodynamics and Spinor Electrodynamics and its coupling to the gravitational field equation. Using Feynman-Gell-Mann equation (second order Dirac equation), the fermionic matter field is nicely incorporated into general theory of relativity with the help of scalar-vector-tensor theory of gravity. Gravitationally coupled spin-field equations and generalized Feynman-Gell-Mann equation are derived from the action proposed here in the article. It is also shown that spin-electromagnetic interaction and spin-spin interaction can curve the space-time.

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The unexpected resurgence of Weyl geometry in late 20-th century physics

Cited by 28 publications

References 0 publications

Weyl geometry, topology of space-time and reality of electromagnetic potentials, and new perspective on particle physics

Weyl geometry, topology of space-time and reality of electromagnetic potentials, and new perspective on particle physics

Geodesic deviation, Raychaudhuri equation, Newtonian limit, and tidal forces in Weyl-type $f(Q,T)$ gravity

Geometrization of Scalar and Spinor Electrodynamics via Bohmian Quantum Gravity

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