Related papers: A revised de Broglie relation in discrete space-ti…
Free bosonic fields are investigated at a classical level by imposing their characteristic de Broglie periodicities as constraints. In analogy with finite temperature field theory and with extra-dimensional field theories, this…
Similarities between the Melvin and Bertotti-Robinson spacetimes are discussed and a uniqueness conjecture is formulated.
We analyze the challenges for inference in difference-in-differences (DID) when there is spatial correlation. We present novel theoretical insights and empirical evidence on the settings in which ignoring spatial correlation should lead to…
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
In this paper we give a discrete version of Hardy's uncertainty principle, by using complex variable arguments, as in the classical proof of Hardy's principle. Moreover, we give an interpretation of this principle in terms of decaying…
We present the constraint for the discrete Moutard equation which gives the integrable discretization of the Bianchi-Ernst system. We also derive the discrete analogue of the Bianchi transformation between solutions of such a system (the…
The purpose of this note is to prove the celebrated Discrete Renewal Theorem in a common special case. We use only very elementary methods from real analysis, rather than markov chain theory, complex analysis, or generating functions.…
In this work, the relativistic phenomena of Lorentz-Fitzgerald contraction and time dilation are derived using a modified distance formula that is appropriate for discrete space. This new distance formula is different than the Pythagorean…
A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of…
In this paper, we discuss several concepts of the modern theory of discrete integrable systems, including: - Time discretization based on the notion of B\"acklund transformation; - Symplectic realizations of multi-Hamiltonian structures; -…
In a purely relational theory there exists a tension between the relational character of the theory and the existence of quantities like distance and duration. We review this issue in the context of the Leibniz-Clarke correspondence. We…
Results concerning the Casimir effect in a topologically closed Minkowski spacetime.
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction.…
Recently a stochastic underpinning for space time has been considered, what may be called Quantized Fractal Space Time. This leads us to a number of very interesting consequences which are testable, and also provides a rationale for several…
A special relativity based on the de Sitter group is introduced, which is the theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary special relativity, it retains the quotient character of…
New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…
A new approach to special relativity is presented which introduces coordinate systems with imaginary time axes, observation systems, and coordinate bases.
The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables…
It is still uncertain whether the cosmic censorship conjecture is true or not. To get a new insight into this issue, we propose the concept of the border of spacetime as a generalization of the spacetime singularity and discuss its…