Related papers: Higher Dimensional Elko Theory
We present four-dimensional gauge theories in Minkowski spacetime which effectively generate in certain energy regimes five-dimensional warped geometries whereas, in general, the fifth dimension is latticized. After discussing in detail…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
A central aim of theoretical physics is to account for the structure of matter at the most elementary level as underlying the Standard Model of particle physics, and ideally also as a basis for a substantial dark sector, as distributed in…
A two-dimensional nonlinear gauge theory that can be proposed for generalization to higher dimensions is derived by means of cohomological arguments.
Beginning from the resolution of the Dirichlet L function, using the inner product formula between two infinite-dimensional vectors in the complex space, the author proved the baffling problem--Hecke conjecture.
In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…
A brief review of the different ways of the Dirac equation derivation is given. The foundations of the relativistic canonical quantum mechanics of a fermionic doublet are formulated. In our approach the Dirac equation is derived from the…
We consider 5D spaces which admit the most symmetric 3D subspaces. 5D vacuum Einstein equations are constructed and 5D analog of the mass function is found. The corresponding conservation law leads to 5D analog of Birkhoff's theorem. Hence…
The consideration of dark energy's quanta, required also by thermodynamics, introduces its chemical potential into the cosmological equations. Isolating its main contribution, we obtain solutions with dark energy decaying to matter or…
We continue the study of the tensor-four-scalars theory which is a modification of general relativity. We include normal matter by applying the displace, cut, and reflect method to our previous vacuum solutions with dark halo. The resulting…
The relativistic positive-energy wave equation proposed by P. Dirac in 1971 is an old but largely forgotten subject. The purpose of this note is to speculate that particles described by this equation (called here Dirac particles) are…
A variety of supergravity and string based models contain hidden sectors which can play a role in particle physics phenomena and in cosmology. In this note we discuss the possibility that the visible sector and the hidden sectors in general…
Dark energy is an elusive concept, which has been introduced two decades ago in order to make the acceleration of the universe a comprehensible phenomenon. However, the nature of this energy is far from being understood, both from a…
In this paper we argue that it is possible to model the Universe along thermodynamic lines, using oscillators in the background Dark Energy at the Planck scale. This leads to meaningful results in agreement with observation.
Gersten has shown how Maxwell equations can be derived from first principles, similar to those which have been used to obtain the Dirac relativistic electron equation. We show how Proca equations can be also deduced from first principles,…
We formulate an exponential Diophantine equation, which is is some sense one order higher that Fermat's Last Theorem. We also give three examples of solutions to this exponential Diophantine equation and formulate a conjecture.
Recently, the first author together with Jens Marklof studied generalizations of the classical three distance theorem to higher dimensional toral rotations, giving upper bounds in all dimensions for the corresponding numbers of distances…
This article investigates higher dimensional vacuum solutions of the Einstein equations. Generalizations of the definitions of spherical and axial symmetry to higher dimensions are discussed before analyzing specific solutions bearing one…
A simple and well-motivated explanation for the origin of dark matter is that it consists of thermal relic particles that get their mass entirely through electroweak symmetry breaking. The simplest models implementing this possibility…
This survey article is an invited contribution to the Encyclopedia of Mathematical Physics, 2nd edition. We provide an accessible overview on relevant applications of higher and derived geometry to theoretical physics, including higher…