Related papers: Lectures on the classical moment problem and its n…
We propose a discussion of angular momentum and its Euler equation, with the aim of giving a short outline of their history. This outline can be useful for teaching purposes too, to amend some problems that students can have in learning…
Contents: Introduction. The Present State of the Universe. What Can We Expect From a Complete Cosmological Theory? An Overview of Quantum Effects in Cosmology. Parametric (Superadiabatic) Amplification of Classical Waves. Graviton Creation…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
We overview our recent studies of cosmological models with expansion and global rotation. Problems of the early rotating models are discussed, and the class of new viable cosmologies is described in detail. Particular attention is paid to…
We provide the differential equations that generalize the Newtonian N-body problem of celestial mechanics to spaces of constant Gaussian curvature, k, for all k real. In previous studies, the equations of motion made sense only for k…
After stating the measurement problem, physicists usually assume the problem to be coming from the measurement part. Since classical probabilities also collapse when updating information, there is nothing special about quantum state…
A problem about the present structure of dimensional analysis, and another one about the differences between solids and fluids are suggested. Both problems appear to have certain foundational aspects.
We indicate a natural generalization of the concept of subgroup commutativity degree of a finite group and a list of open problems on these new concepts.
It is shown, that extended particle-like objects should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytic results concerning the general properties and asymptotic rates of…
The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…
These notes are an elaboration on: (i) a short course that I gave at the IPhT-Saclay in May-June 2012; (ii) a previous letter on reversibility in quantum mechanics. They present an introductory, but hopefully coherent, view of the main…
In this note, we introduce the concept of momentumly closed forms. A nondegenerate momentumly closed two-form defines a moment map that generalizes the classical notion associated with symplectic forms. We then develop an extended theory of…
We examine the classical problem of an infinite square well by considering Hamilton's equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of suitable examples, the nature of the…
We have studied various classical solutions in $R^2$ cosmology. Especially we have obtained general classical solutions in pure $R^2$\ cosmology. Even in the quantum theory, we can solve the Wheeler-DeWitt equation in pure $R^2$\ cosmology…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
The effects of noncommutativity in the phase-space of the classical and quantum cosmology of Bianchi models are investigated. Exact solutions in both commutative and noncommutative cases are presented and compared. Further, the Noether…
We highlight three conflicts between quantum theory and classical general relativity, which make it implausible that a quantum theory of gravity can be arrived at by quantising classical gravity. These conflicts are: quantum nonlocality and…
In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of…
For a 1+1 dimensional theory of gravity with torsion different approaches to the formulation of a quantum theory are presented. They are shown to lead to the same finite dimensional quantum system. Conceptual questions of quantum gravity…
We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…