Related papers: Lectures on the classical moment problem and its n…

These lecture notes intend to form a short pedagogical introduction to inflationary cosmology, highlighting selected areas of recent progress such as reheating and the theory of cosmological perturbations. Problems of principle for…

Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…

We consider the nonrelativistic particle moving on noncommutative space-time in the presence of constant force $\vec{F}$. Further, following the paper M. Daszkiewicz, C.J. Walczyk, Phys. Rev. D 77, 105008 (2008); arXiv: 0802.3575 [math-ph],…

Noncommutativity lays hidden in the proofs of classical dynamics. Modern frameworks can be used to bring it to light: *-products, groupoids, q-deformed calculus, etc.

The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…

These Lectures summarize the relevant material on existent applications of jet manifold techniques to classical and quantum field theory. The following topics are included: 1. Fibre bundles, 2. Jet manifolds, 3. Connections, 4. Lagrangian…

Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…

String Quantum Gravity is motivated and introduced. Advances in the study of the classical and quantum string dynamics in curved spacetime are reported: 1-New Classes of Exact Multistring solutions in curved spacetimes. 2-Mass spectrum of…

This short note is intended to review the foundations of mechanics, trying to present them with the greatest mathematical and conceptual clarity. It was attempted to remove most of inessential, even parasitic issues, which can hide the true…

In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.

I give a review of the conceptual issues that arise in theories of quantum cosmology. I start by emphasising some features of ordinary quantum theory that also play a crucial role in understanding quantum cosmology. I then give motivations…

The time irreversibility problem is the dichotomy of the reversible microscopic dynamics and the irreversible macroscopic physics. This problem was considered by Boltzmann, Poincar\'e, Bogolyubov and many other authors and though some…

This thesis is devoted to studying various aspects of quantum mechanics on non-commutative space-time and to capture some of the surviving aspects of symmetries of quantum field theory on such space-time, illustrated through toy models in…

Classical and quantum aspects of noncommutative field theories are discussed. In particular, noncommutative solitons and instantons are constructed and also d=2,3 noncommutative fermion and bosonic (Wess-Zumino-Witten and…

I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…

An introduction is given to some selected aspects of noncommutative geometry. Simple examples in this context are provided by finite sets and lattices. As an application, it is explained how the nonlinear Toda lattice and a discrete time…

The incompatibility between the treatment of time in the classical and in the quantum theory results in the so-called problem of time in canonical quantum gravity. For this reason, attempts have been made to devise algorithms of…

The canonical formalism of general relativity affords a particularly interesting characterisation of the infamous hole argument. It also provides a natural formalism in which to relate the hole argument to the problem of time in classical…

In this note we collect some known facts concerning central projection correspondances and time parametrizations of Kepler problems in Euclidean spaces and on Spheres.

By applying the nonlinear Legendre transform to the continuity equation, this paper derives exact solutions to the Schr\"odinger equation and the equations of continuum mechanics. A generalized Maxwell distribution has been used as the…