Related papers: Induced gravitation as nonlinear electrodynamics e…
Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short…
A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
We present a survey of the application of Cones' Non-Commutative Geometry to gravitation. Bases of the theory and Euclidian gravity models are reviewed. Then we discuss the problem of a Lorentzian generalization of the theory and review…
The theory of the intrinsic Hall effect, both linear and nonlinear, is rooted in a geometry which is defined in the Bloch-vector parameter space; the formal expressions are mostly derived from semiclassical concepts. When disorder and…
In ultra-clean 2d materials electron viscosity is as important as Ohmic dissipation and electron transport exhibits hydrodynamic features. Using a simple framework of Brinkman equations we find that hydrodynamic electron flows exhibit a…
It is offered that $F(R)-$modified gravities can be considered as nonperturbative quantum effects arising from Einstein gravity. It is assumed that nonperturbative quantum effects gives rise to the fact that the connection becomes…
We use various results concerning isometry groups of Riemannian and pseudo-Riemannian manifolds to prove that there are spaces on which differential structure can act as a source of gravitational force (Brans conjecture). The result is…
Discussed is relationship between nonlinearity and symmetry of dynamical models. The special stress is laid on essential, non-perturbative nonlinearity, when none linear background does exist. This is nonlinearity essentially different from…
Gravitomagnetic effects are characterized by two phenomena: first, the geodetic effect which describes the precession of the spin of a gyroscope in a free orbit around a massive object, second, the Lense-Thirring effect which describes the…
Proposals for nonlinear extenstions of quantum mechanics are discussed. Two different concepts of "mixed state" for any nonlinear version of quantum theory are introduced: (i) >genuine mixture< corresponds to operational "mixing" of…
We present a comprehensive formalism to derive precise expressions for the induced gravity of the braneworld, assuming the dynamics of the Dirac-Nambu-Goto type. The quantum fluctuations of the brane at short distances give rise to…
We explore the new physics phenomena of gravidynamics governed by the inhomogeneous spin gauge symmetry based on the gravitational quantum field theory. Such a gravidynamics enables us to derive the generalized Einstein equation and an…
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
The emission of light pulses is expected to generate gravitational waves, opening the possibility of controlling gravity in an Earthed laboratory. However, measuring the optically-driven spacetime deformations is challenging due to the…
We review nonlinear gauge theory and its application to two-dimensional gravity. We construct a gauge theory based on nonlinear Lie algebras, which is an extension of the usual gauge theory based on Lie algebras. It is a new approach to…
In this essay we marshal evidence suggesting that Einstein gravity may be an emergent phenomenon, one that is not ``fundamental'' but rather is an almost automatic low-energy long-distance consequence of a wide class of theories.…
We survey recent results on inverse problems for geodesic X-ray transforms and other linear and non-linear geometric inverse problems for Riemannian metrics, connections and Higgs fields defined on manifolds with boundary.
Inertial effects play an important role in classical mechanics but have been largely overlooked in quantum mechanics. Nevertheless, the analogy between inertial forces on mass particles and electromagnetic forces on charged particles is not…
Nonlinear analysis has played a prominent role in the recent developments in geometry and topology. The study of the Yang-Mills equation and its cousins gave rise to the Donaldson invariants and more recently, the Seiberg-Witten invariants.…