Related papers: Spherical Relationalism
The Coulomb problem for Schr\"{o}dinger equation is examined, in spaces of constant curvature, Lobachevsky H_{3} and Riemann S_{3} models, on the base of generalized parabolic coordinates. In contrast to the hyperbolic case, in spherical…
We consider scalar tensor theories in D-dimensional spacetime, D \ge 4. They consist of metric and a non minimally coupled scalar field, with its non minimal coupling characterised by a function. The probes couple minimally to the metric…
"Spatial" or "geometric" quantiles are the only multivariate quantiles coping with both high-dimensional data and functional data, also in the framework of multiple-output quantile regression. This work studies spatial quantiles in the…
In a recent paper, algebraic descriptions for all non-relativistic spins were derived by elementary means directly from the Lie algebra $\specialorthogonalliealgebra{3}$, and a connection between spin and the geometry of Euclidean…
At present, our notion of space is a classical concept. Taking the point of view that quantum theory is more fundamental than classical physics, and that space should be given a purely quantum definition, we revisit the notion of Euclidean…
We describe the idea of studying quantum gravity by means of dynamical triangulations and give examples of its implementation in 2, 3 and 4 space time dimensions. For $d=2$ we consider the generic hermitian 1-matrix model. We introduce the…
This work may be defined as a modern philosophical approach to theoretical physics. Since ancient times science and philosophy evolved in parallel, thus renewing from time to time the epochal paradigms of human thought. We could not…
We extend here the canonical treatment of spherically symmetric (quantum) gravity to the most simple matter coupling, namely spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the…
We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
In cosmology, phenomenologically motivated expressions for running vacuum are commonly parametrized as linear functions $\Lambda(H^2)$ or $\Lambda(R)$. Such kind of models assume an equation of state for vacuum given by $\,\overline…
We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subcategory, in which the object is spherical. This general…
The notion of a spherical space over an arbitrary base scheme is introduced as a generalization of a spherical variety over an algebraically closed field. It is studied how the sphericity condition behaves in families. In particular it is…
A $d$--dimensional quantum model in the spherical approximation confined to a general geometry of the form $L^{d-d^{\prime}} \times\infty^{d^{\prime}}\times L_{\tau}^{z}$ ($L$--linear space size and $L_{\tau}$--temporal size) and subjected…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
A class of $k$-Essence cosmological models, with a power law kinetic term, is quantised in the mini-superspace. It is shown that for a specific configuration, corresponding to a pressureless fluid, a Schr\"odinger-type equation is obtained…
The transition from the quantum realm to the classical realm is described in the context of the Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics. We first introduce RBW, discuss its philosophical implications…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
We give from first principles the non-relativistic limit of scalar and Dirac fields in curved spacetime. We aim to find general relativistic corrections to the quantum theory of particles affected by Newtonian gravity, a regime nowadays…
The Schr\"odinger-type formalism of the Klein-Gordon quantum mechanics is adapted for the case of the $SL(2,\R)$ spacetime. The free particle case is solved, the results of a recent work are reproduced while all the other, topologically…