Wannier-Mott excitons in anisotropic or confined systems are studied using the model of
fractional-dimensional space. The excitons in an anisotropic solid are treated as ones in an …

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz
invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows …

Recent findings in the computer sciences, discrete mathematics, formal logics and
metamathematics have opened up a royal road for the investigation of undecidability and …

We propose a model for a power-counting renormalizable field theory living in a fractal
spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The …

Equations of motion are derived for a fractional dimensional system of n-spatial coordinates
to be used as an effective description of anisotropic and confined systems. An existing …

We introduce fractional flat space, described by a continuous geometry with constant non-
integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but …

A bstract We construct a theory of fields living on continuous geometries with fractional
Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski …

A review of different approaches to describe anisotropic fractal media is proposed. In this
paper, differentiation and integration non-integer dimensional and multi-fractional spaces …

We suggest a generalization of vector calculus for the case of non-integer dimensional
space. The first and second orders operations such as gradient, divergence, the scalar and …

arXiv:hep-th/9506171v2 26 Jan 1996 Page 1 arXiv:hep-th/9506171v2 26 Jan 1996 June 8th
1995 hep-th/9506171 PEG-06-95 The Small Scale Structure of Space-Time: A Bibliographical …