Related papers: Interaction from Geometry, Classical and Quantum
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
This article provides a basic introduction to some concepts of non-commutative geometry. The importance of quantum groups and quantum spaces is stressed. Canonical non-commutativity is understood as an approximation to the quantum group…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…
The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues…
There are several regimes in chaotic inflationary cosmology where some part of the system is classical and some other quantum. I describe how to deal with such systems and how to disentangle their dynamics into classical behaviour and…
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…
In this thesis we study the classical and quantum momentum maps and the theory of reduction. We focus on the notion of momentum map in Poisson geometry and we discuss the classification of the momentum map in this framework. Furthermore, we…
In this paper we study new cosmological models involving new forms of non-gravitational interaction between cold dark matter and dark energy. The main purpose is to demonstrate the applicability of the forms of interaction to the problem in…
Geometric properties of operators of quantum Dirac constraints and physical observables are studied in semiclassical theory of generic constrained systems. The invariance transformations of the classical theory -- contact canonical…
I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…
The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a non-equilibrium phase transition into an absorbing state that has been widely investigated and shown to…
Trying to connect a fundamentally non-commutative spacetime with the conservative perturbative approach to quantum gravity, we are led to the natural question: are non-commutative geometrical effects already present in the regime where…
Geometric interactions in a new relativistic geometric unified theory include interactions other than gravitation and electromagnetism. In a low energy limit one of these interactions leads essentially to a Fermi type theory of weak…
An algebraic approach is formulated in the harmonic approximation to describe a dynamics of two-fermion systems, confined in three-dimensional axially symmetric parabolic potential, in an external magnetic field. The fermion interaction is…
The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…
Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that…