Related papers: A Physics of Bounded Metric Spaces
We examine the fundamental question whether a random discrete structure with the minimal number of restrictions can converge to continuous metric space. We study the geometrical properties such as the dimensionality and the curvature…
Some physical aspects of $q$-deformed spacetimes are discussed. It is pointed out that, under certain standard assumptions relating deformation and quantization, the classical limit (Poisson bracket description) of the dynamics is bound to…
We have studied the reconstruction of supersymmetric theories at high scales by evolving the fundamental parameters from the electroweak scale upwards. Universal minimal supergravity and gauge mediated supersymmetry breaking have been taken…
We pose and solve an inverse problem for the classical field equations that arise in the Standard Model of particle physics. Our main result describes natural conditions on the representations, so that it is possible to recover all the…
Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…
We propose a model of a confining dark sector, dark technicolor, that communicates with the Standard Model through the Higgs portal. In this model electroweak symmetry breaking and dark matter share a common origin, and the electroweak…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…
We study gravity coupled to a cosmological constant and a scale but not conformally invariant sector. In Minkowski vacuum, scale invariance is spontaneously broken. We consider small fluctuations around the Minkowski vacuum. At the…
The suggested approach makes it possible to produce a consistent description of motions of a physical system. It is shown that the concept of force fields defining the systems dynamics is equivalent to the choice of the corresponding metric…
Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…
We consider a fairly general class of natural non standard metric products and classify those amongst them, which yield a product of certain type (for instance an inner metric space) for all possible choices of factors of this type (inner…
We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and…
A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
We give a critical analysis of the conceptual foundations of special relativity. We formulate a simple operational criterion for distinguishing between noninertial and inertial frames which is introduced prior to geometry. We associate the…
Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data and with compositional data, like percentages and the like. If the natural measure of difference is not the absolute…
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
The emergence of a classical spacetime from any quantum gravity model is still a subtle and only partially understood issue. If indeed spacetime is arising as some sort of large scale condensate of more fundamental objects then it is…
For a real or complex one-dimensional map satisfying a weak hyperbolicity assumption, we study the existence and statistical properties of physical measures, with respect to geometric reference measures. We also study geometric properties…
In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric…