Related papers: A Physics of Bounded Metric Spaces
Minkowski's classical existence theorem provides necessary and sufficient conditions for a Borel measure on the unit sphere of Euclidean space to be the surface area measure of a convex body. The solution is unique up to a translation. We…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Since the end of the 19th century, and after the works of F. Klein and H. Poincar\'e, it is well known that models of elliptic geometry and hyperbolic geometry can be given using projective geometry, and that Euclidean geometry can be seen…
We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of…
A framework is suggested in which the energy integrals of the Friedmann cosmology are identified as genuine time-independent physical characteristics for both vacuum and non-vacuum forms of cosmic energy. The integrals are found to be…
An explicit dynamical model for non relativistic quantum mechanics with an effective gravitational interaction is proposed, which, as being well defined, allows in principle for the evaluation of every physical quantity. Its non unitary…
The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…
We derive the gravitational and electrostatic self-energies of a particle at rest in the background of a cosmic dispiration (topological defect), finding that the particle may experience potential steps, well potentials or potential…
We further investigate postulates for realist versions of relativistic quantum theory and quantum field theory in Minkowski space and other background space-times. According to these postulates, quantum theory is supplemented by local…
It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do…
In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
The dynamics of a quantum mechanical particle in a time-independent potential are found to contain many interesting phenomena. These are direct consequences of the (typical) existence of more than one time scale governing the problem. This…
A generalised equivalence principle is put forward according to which space-time symmetries and internal quantum symmetries are indistinguishable before symmetry breaking. Based on this principle, a higher-dimensional extension of Minkowski…
We incorporate metric data into the framework of Tannaka-Krein duality. Thus, for any group with left invariant metric, we produce a dual metric on its category of unitary representations. We characterize the conditions under which a…
We study some aspects when one consider the existence of one extra-dimension in addition to a non-commutative space-time. We present here two different examples, where the first one provides a scenario were it is possible to relate the…
We show that, in the framework of Deformed Special Relativity (DSR), namely a (four-dimensional) generalization of the (local) space-time struc- ture based on an energy-dependent "deformation" of the usual Minkowski geometry, two kinds of…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
In this paper, we introduce the $\mathcal{F}$-metric space concept, which generalizes the metric space notion. We define a natural topology $\tau_{\mathcal{F}}$ in such spaces and we study their topological properties. Moreover, we…