Related papers: Free motion in deformed (quantum) four-dimensional…
Examination of the Einstein energy-momentum relationship suggests that simple unbound forms of matter exist in a four-dimensional Euclidean space. Position, momentum, velocity, and other vector quantities can be expressed as Euclidean…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and…
It is possible that relativistic symmetries become deformed in the semiclassical regime of quantum gravity. Mathematically, such deformations lead to the noncommutativity of spacetime geometry and non-vanishing curvature of momentum space.…
A covariant hamiltonian formalism for the dynamics of compact spinning bodies in curved space-time in the test-particle limit is described. The construction allows a large class of hamiltonians accounting for specific properties and…
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…
The extremely fascinating behaviors of the quantum walks of particles, which differ much from the classical counterparts, have attracted many physicists. Here we investigate another interesting part of the quantum walks, that is the quantum…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional…
Bodies in relative motion, spatially separated in vacuum, experience a tiny friction force known as quantum friction. This force has eluded experimental detection so far due to its small magnitude and short range. Herein, we give…
The kinematics of particles moving in rainbow spacetime is studied in this paper. In particular the geodesics of a massive particle in rainbow flat spacetime is obtained when the semi-classical effect of its own energy on the background is…
The FRT quantum group and space theory is reformulated from the standard mathematical basis to an arbitrary one. The $N$-dimensional quantum vector Cayley-Klein spaces are described in Cartesian basis and the quantum analogs of…
We argue that the conventional quantum field theory in curved spacetime has a grave drawback: The canonical commutation relations for quantum fields and conjugate momenta do not hold. Thus the conventional theory should be denounced and the…
Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space-time symmetries of the corresponding equations of motion. A systematic analysis of…
A quantum Schwarzschild spacetime and a quantum Schwarzschild-de Sitter spacetime with cosmological constant $\Lambda$ are constructed within the framework of a noncommutative Riemannian geometry developed in an earlier publication. The…
We discuss quantum dynamics in multi-dimensional non-linear systems. It is well-known that wave functions are localized in a kicked rotor model. However, coupling with other degrees of freedom breaks the localization. In order to clarify…
It has been argued that an extended, quasi-rigid body evolving freely in curved spacetime can deviate from its natural trajectory by simply performing cyclic deformations. More interestingly, in the limit of rapid cycles, the amount of…
A quantum-mechanical theory of gravitation is presented, where the motion of particles is based on the optics of de Broglie waves. Here the large-scale geometry of the universe is inherently flat, and its age is not constrained to < 13 Gyr.…
I extend the three-dimensional q-deformed Euclidean space by a time element and discuss the algebraic structure of this quantum space together with its differential calculi. Using the star-product formalism, I will give basic operations of…