相关论文: A revised de Broglie relation in discrete space-ti…

In this letter we briefly investigate the mathematical structure of space-time in the framework of discretization. It is shown that the discreteness of space-time may result in a new mechanical system which differ from the usual quantum…

We review some modern theories about the structure of space and time, in particular those related to discrete space and time. Following an epistemological method we start from theories which discuss discrete space and time as a mathematical…

We put forward a model of discrete physical space that can account for the structure of space- time, give an interpretation to the postulates of quantum mechanics and provide a possible explanation to the organization of the standard model…

Relative motion of particles is examined in the context of relational space-time. It is shown that de Broglie waves may be derived as a representation of the coordinate maps between the rest-frames of these particles. Energy and momentum…

We give a theory of sublinear expectations and martingales in discrete time. Without assuming the existence of a dominating probability measure, we derive the extensions of classical results on uniform integrability, optional stopping of…

The possibility that time can be regarded as a discrete parameter is re-examined. We study the dynamics of the free particle and find in some cases superluminal propagation.

We study a general family of space-time discretizations of the KPZ equation and show that they converge to its solution. The approach we follow makes use of basic elements of the theory of regularity structures [M. Hairer, A theory of…

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the…

We discuss alternatives to the usual quantization of relativistic particles which result in discrete spectra for position and time operators.

Based on a new idea of factorization, we prove an improved discrete Rellich inequality and discuss its optimality. We also give a conjecture on improved higher order discrete Hardy-like inequalities and formulate an open problem for the…

In this contribution we use the model of discrete spaces that we have put forward in former articles to give an interpretation to the phenomena of quantum entanglement and quantum states reduction that rests upon a new way of considering…

We survey some results about the asymptotic behavior of discrete spacetime models, which appeared in diverse settings in the physics and math literature. We then discuss some recent applications, including scheduling in disk drives and…

We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of…

This is a survey note of the author's observations on the discrete-time analogues of It\^o formulas.

We study the stochastic $p$-Laplace system in a bounded domain. We propose two new space-time discretizations based on the approximation of time-averaged values. We establish linear convergence in space and $1/2$ convergence in time.…

In this work, the relativistic phenomena of Lorentz contraction and time dilation are derived using a modified distance formula appropriate for discrete space. This new distance formula is different than Pythagoras's theorem but converges…

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.

In this paper we show the connection between the q-deformation and discrete time, starting from the q-deformed Heisenberg uncertainty relation and q-deformation calculus. We show that time has discrete nature and for this case we construct…

Fractional calculus represents a natural tool for describing relativistic phenomena in pseudo-Euclidean space-time. In this study, Fractional modified special relativity is presented. We obtain fractional generalized relation for the time…

A discretization of the peakons lattice is introduced, belonging to the same hierarchy as the continuous--time system. The construction examplifies the general scheme for integrable discretization of systems on Lie algebras with $r$--matrix…