Related papers: The Many Dimensions of Dimension
This note is devoted to a detail concerning the work of Albert Einstein and Peter Bergmann on unified theories of electromagnetism and gravitation in five dimensions. In their paper of 1938, Einstein and Bergmann were among the first to…
We review the relation between scale and conformal symmetries in various models and dimensions. We present a dimensional reduction from relativistic to non-relativistic conformal dynamics.
We investigate, in Randall-Sundrum braneworld scenario, the relationship between perturbations of gravitational and electromagnetic waves in a black hole neighboorhood, proposing an extra-dimensional braneworld extension of the traditional…
We attempt to reformulate eleven dimensional supergravity in terms of an object that unifies the three-form and the metric and makes the M-theory duality group manifest. This short note deals with the case of where the U-duality group…
These five lectures collect elementary facts about 4D supersymmetric theories with emphasis on N=1 supersymmetry, as well as the basic notions of supersymmetric quantum mechanics. Contents: I. From symmetries to supersymmetry; II. Basic…
We discuss renormalizability of a recently established, massive gravity theory with particular higher derivative terms in three space-time dimensions. It is shown that this massive gravity is certainly renormalizable as well as unitary, so…
Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…
A thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential and the…
Dimensional reduction from 10 to 5 dimensions of the IIB supergravity Dirac equation written down on the AdS(5)xS(5) (+ self-dual 5-form) background provides the unambiguous values of bulk masses of Fermions in the effective 5D Randall…
It was recently proposed that five-dimensional inflation can relate the causal size of the observable universe to the present weakness of gravitational interactions by blowing up an extra compact dimension from the microscopic fundamental…
The quest for unification of particles and fields and for reconciliation of Quantum Mechanics and General Relativity has led us to gauge theories, string theories, supersymmetry and higher-extended objects: membranes... Our spacetime is…
An overview of matter-coupled ${\cal N}=2$ supergravity theories with 8 real supercharges, in 4,5 and 6 dimensions is given. The construction of the theories by superconformal methods is explained from basic principles. Special geometry is…
Theories of partial supersymmetry breaking N=2 -> N=1 in four dimensions are derived by coupling the N=2 massless gravitino multiplet to N=2 supergravity in five dimensions and performing a generalized dimensional reduction on S^1/Z_2 with…
This article is an introductory work to a larger research project devoted to pure, applied and philosophical aspects of dimension theory. It concerns a novel approach toward an alternate dimension theory foundation: the point-dimension…
We consider variation of coupling strengths and mass ratios in and beyond the Standard Model, in the light of various mechanisms of mass generation. In four-dimensional unified models, variations in charged particle thresholds, light quark…
A geometric formulation which describes extended supergravities in any dimension in presence of electric and magnetic sources is presented. In this framework the underlying duality symmetries of the theories are manifest. Particular…
We are going to introduce a new algebraic, analytic structure that is a kind of generalization of the Hausdorff dimension and measure. We give many examples and study the basic properties and relations of such systems.
We presented a model for unification of electricity and gravity. We have found a consistent description of all physical quantities pertaining to the system. We have provided limiting values for all physical values. These values are neither…
Dimensional regularization is used to derive the equations of motion of two point masses in harmonic coordinates. At the third post-Newtonian (3PN) approximation, it is found that the dimensionally regularized equations of motion contain a…
We extend the classical general relativistic theory of measurement to include the possibility of existence of higher dimensions. The intrusion of these dimensions in the spacetime interval implies that the inertial mass of a particle in…