Related papers: Lectures on the classical moment problem and its n…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is…
The application of a classical approach to various quantum problems - the secular perturbation approach to quantization of a hydrogen atom in external fields and a helium atom, the adiabatic switching method for calculation of a…
This contribution analyses the classical laws of motion by means of an approach relating time and entropy. We argue that adopting the notion of change of states as opposed to the usual derivation of Newton's laws in terms of fields a…
This paper gives an elementary introduction to some of the conceptual problems of quantum cosmology. Contents: 1. Why quantum cosmology? 2. Time in quantum gravity 3.Decoherence and the recovery of the Schrodinger equation 4. The direction…
Angular momentum in classical and quantum mechanics is carried out beyond textbooks frames. We compare angular distribution of particle position with classical probabilistic approach. Addition of angular momenta is also discussed together…
In this book, we review various aspects of the Lorentz symmetry breaking, both classical and quantum ones, with the special interest to perturbative generation of Lorentz-breaking terms. We present impacts of Lorentz symmetry breaking in…
This is the extended version of a talk presented at the J.W.Goethe Universitaet Frankfurt a. M. and at the same time a preview at a forthcoming extensive publication on the same subject. It is shown that there is a common background…
A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…
These lecture notes cover classical undecidability results in number theory, Hilbert's 10th problem and recent developments around it, also for rings other than the integers. It also contains a sketch of the authors result that the integers…
We study the classical dynamics of non-relativistic particles endowed with spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which…
In these notes we present a selection of topics, each section approximately amounting to one lecture. We begin with a brief recapitulation of General Relativity, and the Standard Model of Cosmology. This is followed by lectures on important…
Decoherence and the approach to the classical final limit are studied in two similar cases: the Mott and the Cosmological problems.
The book covers basics of noncommutative geometry and its applications in topology, algebraic geometry and number theory. A brief survey of main parts of noncommutative geometry with historical remarks, bibliography and a list of exercises…
These notes are connected to a "potpourri" topics class and deal with some special cases of norms of various objects which arise in classical analysis.
This paper reviews results about discrete physics and non-commutative worlds and explores further the structure and consequences of constraints linking classical calculus and discrete calculus formulated via commutators. In particular we…
These are lecture notes, which summarize the current status of the Semiclassical theory, as well as Monopoles, Instantons, Instanton-dyons and Flux tubes. The emphasis is on QCD and QCD-like theories (deformed QCD), although relevant points…
The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of…
One approach for formulating the classical dynamics of charged particles in non-Abelian gauge theories is due to Wong. Following Wong's approach, we derive the classical equations of motion of a charged particle in U(1) gauge theory on…
The problem of unification of Gravitation and Electromagnetism in four dimensions; some new ideas involving mixtures of commuting and anti-commuting co-ordinates. Maxwell's equations are extracted in terms of the curvature of the…