Related papers: Free motion in deformed (quantum) four-dimensional…
We argue that theories of quantum gravity constructed with the help of (Causal) Dynamical Triangulations have given us the most informative, quantitative models to date of quantum spacetime. Most importantly, these are derived dynamically…
This conference talk elaborates on a recently discovered mapping procedure by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed correctly into those in curved space. This procedure…
We propose the model of massive spinning particle traveling in four-dimensional Minkowski space. The equations of motion of the particle follow from the fact that all the classical paths of the particle lie on a cylinder whose position in…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth…
A selfconsistent definition of quantum free particle on a generic curved manifold emerges naturally by restricting the dynamics to submanifolds of co-dimension one. PACS 0365 0240
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
We discuss a new realistic interpretation of quantum mechanics based on discontinuous motion of particles. The historical and logical basis of discontinuous motion of particles is given. It proves that if there exists only one kind of…
The complex unit appearing in the equations of quantum mechanics is generalised to a quaternionic structure on spacetime, leading to the consideration of complex quantum mechanical particles whose dynamical behaviour is governed by…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov--Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The…
We discuss the phase structure of a higher derivative four-fermion model in four dimensions in curved spacetime in frames of the $\frac{1}{N_c}$-expansion. First, we evaluate in our model the effective potential of two composite scalars in…
Relational formulations of classical mechanics and gravity have been developed by Julian Barbour and collaborators. Crucial to these formulations is the notion of shape space. We indicate here that the metric structure of shape space allows…
Influence of noncommutativity on the motion of composite system is studied in noncommutative phase space of canonical type. A system composed by $N$ free particles is examined. We show that because of momentum noncommutativity free…
We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface. For the Gaussian bump we derive and discuss the quantum potential which results in the appearance of a bound state for particles with…
We present a quantum deformation theory of the Airy curve and use it to establish a version of mirror symmetry of a point.
The Newton equation describing the particle motion in constant external field force on canonical, Lie-algebraic and quadratic space-time is investigated. We show that for canonical deformation of space-time the dynamical effects are absent,…
We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time…