相关论文: Deformation principle as a foundation of physical …

A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two…

When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…

In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…

Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…

We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose quantum parameter has the physical…

We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…

The Newton equation describing the particle motion in constant external field force on canonical, Lie-algebraic and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent,…

Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…

Quantum gravity phenomenology suggests an effective modification of the general relativistic dispersion relation of freely falling point particles caused by an underlying theory of quantum gravity. Here we analyse the consequences of…

The geometric concept of geodesic completeness depends on the choice of the metric field or "metric frame". We develop a frame-invariant concept of "generalised geodesic completeness" or "time completeness". It is based on the notion of…

Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…

This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…

Minimal and maximal uncertainties of position measurements are widely considered possible hallmarks of low-energy quantum as well as classical gravity. While General Relativity describes interactions in terms of spatial curvature, its…

This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or…

We present a way of understanding the curvature of space-time, the basic philosophy being that the (linear) geometry of any space is determined by the (linear) functionals on the algebra(s) of any fields defined on the space. It is known…

This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…

We investigate the application of deformation quantization to the system of a free particle evolving within a universe described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. This approach allows us to analyze the dynamics of…

Classical gravity can be described as a relational dynamical system without ever appealing to spacetime or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles…

The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the…

The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum…