Related papers: A Few Comments on Classical Electrodynamics
The paper discusses an applicability criterion for a cutoff regularization in the coordinate representation in the Euclidean space with a dimension larger than two. It is shown that the set of functions satisfying the criterion is not…
We use astrophysical data to shed light on fundamental physics by constraining parametrized theoretical cosmological and gravitational models. Gravitational parameters are those constants that parametrize possible departures from Einstein's…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
Relativity is an integral part of positioning systems, and this is taken into account in today's practice by applying many "relativistic corrections" to computations performed using concepts borrowed from Galilean physics. A different,…
Interaction of spin with electromagnetic field yields an effective metric along the world line of spinning particle. If we insist to preserve the usual special-relativity definitions of time and distance, critical speed which spinning…
We discuss a particular problem of enumerating rational curves on a Grassmannian from several perspectives, including systems theory, real enumerative geometry, and symbolic computation. We also present a new transversality result, showing…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
We explore the characteristics of shadows for a general class of spherically symmetric, static spacetimes, which may arise in general relativity or in modified theories of gravity. The chosen line element involves a sum (with constant but…
The cosmological constant problem can be understood as the failure of the decoupling principle behind effective field theory, so that some quantities in the low-energy theory are extremely sensitive to the high-energy properties. While this…
It is shown that properties of a discrete space-time geometry distinguish from properties of the Riemannian space-time geometry. The discrete geometry is a physical geometry, which is described completely by the world function. The discrete…
The concept of a physical space, which actualizes Euclidean geometry, is not confined to the statics of solids but extensible to the phenomena where Newtonian mechanics is valid, defining its concept of time. The laws of propagation of…
Euclidean space and linear algebra do not characterize dynamic electronic orbitals satisfactorily for even the motion of both electrons in an inert helium atom cannot be defined in reasonable details. Here the author puts forward a novel…
This thesis addresses two major problems in the philosophy of physics. The first is how to identify the minimal physical content of a theory; that is, what features of a theory are truly needed to make predictions, and what can be removed…
In these lectures, I discuss the role of symmetries in particle physics. I begin by discussing global symmetries and show that they can be realized differently in nature, depending on whether or not the vacuum state is left invariant by the…
General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory…
The equivalence of a conformal metric on 4-dimensional space-time and a local field of 3-dimensional subspaces of the space of 2-forms over space-time is discussed and the basic notion of transection is introduced. Corresponding relation is…
We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such…
This paper concerns the \textbf{abstract geometry of numbers}: namely the pursuit of certain aspects of geometry of numbers over a suitable class of normed domains. (The standard geometry of numbers is then viewed as geometry of numbers…
We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the…
We will look for an implementation of new symmetries in the space-time structure and their cosmological implications. This search will allow us to find a unified vision for electrodynamics and gravitation. We will attempt to develop a…