Fractal extra dimension in Kaluza-Klein theory

  title={Fractal extra dimension in Kaluza-Klein theory},
  author={Igor I. Smolyaninov},
  journal={Physical Review D},
Kaluza-Klein theory in which the geometry of an additional dimension is fractal is considered. In such a theory the mass of an elementary electric charge appears to be many orders of magnitude smaller than the Planck mass, and the ``tower'' of masses which correspond to higher integer charges becomes aperiodic. 

The Casimir Effect for Parallel Plates in the Spacetime with a Fractal Extra Compactified Dimension

The Casimir effect for massless scalar fields satisfying Dirichlet boundary conditions on the parallel plates in the presence of one fractal extra compactified dimension is analyzed. We obtain the

Quantum gravity, field theory and signatures of noncommutative spacetime

A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of

Casimir Effect at Finite Temperature in the Presence of One Fractal Extra Compactified Dimension

We discuss the Casimir effect for massless scalar fields subject to the Dirichlet boundary conditions on the parallel plates at finite temperature in the presence of one fractal extra compactified

Extra-Dimensional “Metamaterials”: A Model of Inflation Due to a Metric Signature Transition

Lattices of topological defects, such as Abrikosov lattices and domain wall lattices, often arise as metastable ground states in higher-dimensional field theoretical models. We demonstrate that such

Non-local Optical Topological Transitions and Critical States in Electromagnetic Metamaterials

This work uncovers a new class of optical topological transitions in metamaterials, induced by the non-locality of the electromagnetic response inherent to these composites.

Seiberg-Witten maps for SO(1,3) gauge invariance and deformations of gravity

A family of diffeomorphism-invariant Seiberg-Witten deformations of gravity is constructed. In a first step Seiberg-Witten maps for an SO(1,3) gauge symmetry are obtained for constant deformation

Holographic duality in nonlinear hyperbolic metamaterials

According to the holographic principle, the description of a volume of space can be thought of as encoded on its boundary. Holographic principle establishes equivalence, or duality, between

Five-Dimensional Spacetimes Emulated with Metamaterials

We demonstrate that optical space in metamaterials may be engineered to mimic physics in a five-dimensional (5D) spacetime. Two metamaterial-based models of 5D spacetimes have been considered. The

Metamaterial ‘multiverse’

Optical space in metamaterials may be engineered to mimic the landscape of a multi-dimensional universe which has regions of different topology and different effective dimensionality. This



Fractals: Form, Chance and Dimension

This is the most extraordinarily beautiful book in thought and in form that I have read for many years, and that is all the more peculiar for its being a somewhat technically mathematical treatise.


  • Acad. Wiss. K 1, 966 (1921); O. Klein, Z.Phys. 37, 895
  • 1926