Related papers: Generalized Statistics and Dynamics in Curved Spac…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
If universal quantum interaction is really connected with the coset structure of deformations of quantum states then the curvature of projective Hilbert state space should be observable. I discuss some approach to the measurement of…
We find explicit solutions of the Heisenberg equations of motion for a quadratic Hamiltonian, describing a generic model of variable media, in the case of multi-parameter squeezed input photon configuration. The corresponding probability…
Diverse theories of Quantum Gravity expect modification of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle.It was shown by some authors that the Generalized uncertainty principle…
A discussion of relativistic quantum-geometric mechanics on phase space and its generalisation to the propagation of free, massive, quantum-geometric scalar fields on curved spacetimes is given. It is shown that in an arbitrary coordinate…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
In this review article we present different formal frameworks for the description of generalized probabilities in statistical theories. We discuss the particular cases of probabilities appearing in classical and quantum mechanics, possible…
We revisit the issue of time in quantum geometrodynamics and suggest a quantization procedure on the space of true dynamic variables. This procedure separates the issue of quantization from enforcing the constraints caused by the general…
We investigate homogeneity in the special Colombeau algebra. It is shown that strongly scaling invariant functions on the d-dimensional space are simply the constants. On the pierced space, strongly homogeneous functions admit tempered…
A theory in which points, lines, areas and volumes are on on the same footing is investigated. All those geometric objects form a 16-dimensional manifold, called C-space, which generalizes spacetime. In such higher dimensional space…
Continuous symmetries generated with observables of a quantum theory in the Minkowski spacetime are discussed. An example of an originated in this way algebra of observables is the algebra of observables of the canonical quantum theory,…
Scaling properties inherent in quantum dynamics have been studied for various systems in terms of acceleration, deceleration and time reversing. We show a scaling property of quantum dynamics on curved space-time where gravity plays an…
\noindent We briefly discuss some algebraic and geometric aspects of the generalized Poisson bracket and non--commutative phase space for generalized quantum dynamics, which are analogous to properties of the classical Poisson bracket and…
The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
Complicated time-dependent curved spacetime and electric field are involved in many astrophysical situations, including the early universe, Hawking radiation, the Schwinger effect, and gravitational pair production. In this Letter, a…
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a…
This article aims to explain some of the basic facts about the questions raised in the title, without the technical details that are available in the literature. We provide a gentle introduction to some rather classical results about…
We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In…
In this study, we consider curves of generalized AW(k)-type of Euclidean n-space. We give curvature conditions of these kind of curves.