Related papers: Discrete space-time geometry and skeleton concepti…

We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…

We show that the following elementary geometric properties of the motion of a discrete (i.e. piecewise linear) curve select the integrable dynamics of the Ablowitz-Ladik hierarchy of evolution equations: i) the set of points describing the…

Physical time intervals are attributes of single physical object whereas physical space intervals are a relational attribute of two physical objects. Some consequences of the breaking of the space-time exchange symmetry inherent in the…

We show that for non-relativistic free particles, the (bosonic) many particle equations can be rewritten in geometric fashion in terms of a classical theory of conformally stretched spacetime. We further generalize the results for the…

The Old Quantum Mechanics actions discretization rules for periodic motions on the atomic scale (Bohr-Sommerfeld) have been suitably modified in order to account the gravitational field instead of the electrostatic one. The new rules are…

We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…

The incorporation of an adequate discrete expansion to the formalism of the special relativity that does not allow gravitational acceleration unravels unexplored phenomena. This extension takes into account consequences of a small variation…

This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains,…

We develop the spectral point of view on geometry based on the formalism of quantum physics. We start from the simple physical question of specifying our position in space and explain how the spectral geometric point of view provides a new…

Given a trivalent graph in the 3-dimensional Euclidean space, we call it a discrete surface because it has a tangent space at each vertex determined by its neighbor vertices. To abstract a continuum object hidden in the discrete surface, we…

It is shown that the differential geometry of space-time, can be expressed in terms of the algebra of operators on a bundle of Hilbert spaces. The price for this is that the algebra of smooth functions on space-time has to be made…

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…

Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…

In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…

We present a new description of discrete space-time in 1+1 dimensions in terms of a set of elementary geometrical units that represent its independent classical degrees of freedom. This is achieved by means of a binary encoding that is…

Special relativity turns out to be more than coordinate transformations in which the constancy of the speed of light plays the central role between two inertial reference frames. Special relativity, in essence, is a theory of…

In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…

Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those which do not thermalize under…

At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general…

This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…