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If spacetime possesses extra dimensions of size and curvature radii much larger than the Planck or string scales, the dynamics of these extra dimensions should be governed by classical general relativity. We argue that in general…
We suggest an alternative mathematical model for the electron in dimension 1+2. We think of our (1+2)-dimensional spacetime as an elastic continuum whose material points can experience no displacements, only rotations. This framework is a…
An analysis of the concept of orientation used in electrodynamics is presented. At least two different versions are encountered in the literature. Both are clearly identified and comparisons are made.
We present an overview of a theory of complex dimensions of self-similar fractal strings, and compare this theory to the theory of varieties over a finite field from the geometric and the dynamical point of view. Then we combine the several…
In the work by T. Duyckaerts and F. Merle, they studied the variational structure near the ground state solution $W$ of the energy critical wave equation and classified the solutions with the threshold energy $E(W,0)$ in dimensions…
Superstring theories in the critical dimension D=10 are connected to one another by a well-explored web of dualities. In this paper we use closed-string tachyon condensation to connect the supersymmetric moduli space of the critical…
An eigenvalue equation representing symmetric (dual) quantum equation is introduced. The particle is described by two scalar wavefunctions, and two vector wavefunctions. The eigenfunction is found to satisfy the quantum Telegraph equation…
Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…
We study the classical cosmic string solution in a theory with dynamical $U(1)$ symmetry breaking. We calculate the energy per unit length of the string and compare it to that obtained in a model with a fundamental Higgs. We find that the…
This article briefly summarizes and reviews the motivations for - and the present status of - the proposal that the small size of the observed Dark Energy density can be understood in terms of the dynamical relaxation of two large extra…
The issue of a self-consistent solution of Maxwell-Einstein equations achieves a very simple form when all quantum effects are neglected but a weak vacuum polarization due to an external magnetic field is taken into account. From a…
String theory and supersymmetry are theoretical ideas that go beyond the standard model of particle physics and show promise for unifying all forces. After a brief introduction to supersymmetry, we discuss the prospects for its experimental…
We review some of the recent work on the dynamics of four dimensional, supersymmetric gauge theories. The kinematics are largely determined by holomorphy and the dynamics are governed by duality. The results shed light on the phases of…
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light…
Dimension-varying linear systems are investigated. First, a dimension-free state space is proposed. A cross dimensional distance is constructed to glue vectors of different dimensions together to form a cross-dimensional topological space.…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
Minkowski spacetime is a convenient setting for the study of the relativistic dynamics of particles and fields in the vacuum. In order to study events that occur in a dielectric or other linear medium, we adopt the familiar continuum…
In this paper we consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. The latter consists only of two constant states, where one state lies on the lower and the other state on…
A string theory in $3$ euclidean spacetime dimensions is found to describe the semiclassical behavior of a certain exact physical state of quantum general relativity in $4$ dimensions. Both the worldsheet and the three dimensional metric…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…