Related papers: The Many Dimensions of Dimension
We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational…
A null path in 5D can appear as a timelike path in 4D, and for a certain gauge in 5D the motion of a massive particle in 4D obeys the usual quantization rule with an uncertainty-type relation. Generalizations of this result are discussed in…
I address the issue of spacetime dimensionality within Kaluza-Klein theories and theories with large extra dimensions. I review the arguments explaining the dimensionality of the universe, within the framework of string gas cosmology and…
A recent result concerning interacting theories of self-dual tensor gauge fields in six dimensions is generalized to include coupling to gravity. The formalism makes five of the six general coordinate invariances manifest, whereas the sixth…
In the effective field theory framework, quantum gravity can induce effective dimension-5 operators, which have important impacts on grand unified theories. Interestingly, one of main effects is the modification of the usual gauge coupling…
Consider the minimal renormalizable extension of the Standard Model with purely dimensionless couplings, successful electroweak symmetry breaking (via the Coleman-Weinberg mechanism) and a see-saw mechanism for neutrino mass: we will call…
The construction of the linearized four-dimensional multisupergravity from five-dimensional linearized supergravity with discretized fifth dimension is presented. The one-loop vacuum energy is evaluated when (anti)periodic boundary…
According to modern quantum physics, at the microlevel, the dimension of space-time is at least 11; we only observe 4 dimensions because the others are compactified: the size along each of the other dimensions is much smaller than the…
We consider a two-time (characterized by distinct speeds of causality) and three-space-dimensional Minkowski space and derive relativistic coordinate and velocity transformation formulas and expressions for a new effective speed limit.…
The basic quasi-Schwarzschild 5D objects known as solitons have a long history, which is reviewed. Then some material is added, leading to the inference that a soliton is a singularity in the geometry which represents a bivalent source of…
The matrix model computations of effective superpotential terms in N=1 supersymmetric gauge theories in four dimensions have been proposed to apply more generally to gauge theories in higher dimensions. We discuss aspects of…
Dimensional analysis provides many simple and useful tools for various situations in science. The objective of this paper is to investigate its relations to functions, i.e., the dimensions for functions that yield physical quantities and…
The purpose of this contribution is to elucidate some of the properties of Shape Dynamics (SD) and is largely based on a recent longer article. We shall point out some of the key differences between SD and related theoretical constructions,…
First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear…
In this Letter, we propose a new scenario emerging from the conjectured presence of a minimal length $\ell$ in the spacetime fabric, on the one side, and the existence of a new scale invariant, continuous mass spectrum, of un-particles on…
Recent developments in supersymmetric unified theories are reviewed, with particular emphasis on supersymmetric grand unification and a brief discussion of recent ideas about extra dimensions.
An introduction to Seiberg-Witten theory and its relation to theories which include gravity.
In two dimensions a large class of gravitational systems including, e.g., $R^2$-gravity can be quantized exactly also when coupled dynamically to a Yang-Mills theory. Some previous considerations on the quantization of pure gravity theories…
The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the field of analytic complex functions, the generic…
Exploring the recent expansion history of the universe promises insights into the cosmological model, the nature of dark energy, and potentially clues to high energy physics theories and gravitation. We examine the extent to which precision…