Related papers: Intrinsic Kinematics
We examine the motion of a relativistic charged particle in a constant magnetic field perturbed by gravitational waves incident along the direction of the magnetic field. We apply a generalized energy conservation law to compute the…
We construct the isospin particle system on $n$-dimensional quaternionic projective spaces in the presence of BPST-instanton by the reduction from the free particle on $(2n+1)$-dimensional complex projective space. Then we add to this…
We introduce the concept of extrinsic catenary in the hyperbolic plane. Working in the hyperboloid model, we define an extrinsic catenary as the shape of a curve hanging under its weight as seen from the ambient space. In other words, an…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
By means of the Minlos Theorem on support of cylindrical measures on vectorial topological spaces, we present several results on the rigorous definitions of Euclidean path integrals and applications to some problems on non-linear diffusion,…
Rapidly rotating bodies moving in curved space-time experience the so-called spin-curvature force, which becomes important for the motion of compact objects in gravitational-wave inspirals. As a first approximation, this effect is captured…
The gravitational couplings of intrinsic spin are briefly reviewed. A consequence of the Dirac equation in the exterior gravitational field of a rotating mass is considered in detail, namely, the difference in the energy of a spin-1/2…
Protocols for observing gravity induced entanglement typically comprise the interaction of two particles prepared either in a superposition of two discrete paths, or in a continuously delocalized (harmonic oscillator) state of motion. An…
In our previous work (Phys. Rev. Research 7, 033079), we derived the metric tensor for cylindrically shaped pulses with uniform energy density. Building upon that framework, we derive the complete set of geodesics with zero angular…
Applying the perturbative approach to geodesic equations, we study motion of the test particles in time-dependent spherically symmetric spacetimes created by oscillating dark matter. Assuming the weakness of the gravitational field, we…
In this paper we present a stepwise construction of the path integral over relativistic orbits in Euclidean spacetime. It is shown that the apparent problems of this path integral, like the breakdown of the naive Chapman-Kolmogorov…
Motion of test particles along rotating curved trajectories is considered. The problem is studied both in the laboratory and the rotating frames of reference. It is assumed that the system rotates with the constant angular velocity $\omega…
We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space which evolve by an arbitrary (non-homogeneous) function of the radii of curvature. The associated flow of the radii of…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other, and then are entangled in the…
An interesting phenomenon that occurs in projectile motion, the "coming and going", is analyzed considering linear air resistance force. By performing both approximate and numerical analysis, it is showed how a determined critical angle and…
One of several possibilities to construct a quantum theory of gravity is employing the Feynman path integral. This approach is plagued by some problems: the integration measure is not uniquely defined, the Einstein-Hilbert action unbounded,…
Mechanics texts tell us that a particle in a bound orbit under gravitational central force moves on an ellipse, while introductory physics texts approximate the earth as flat, and tell us that the particle moves in a parabola. The…
The present paper discusses certain special Gaussian beams that, thanks to some polynomial prefactors, have uniquely designed holes in the irradiance. Such holes, or rather tubes, can constitute potential valleys for negatively polarizable…
We present an introduction to the study of a relativistic particle moving under the influence of its own Frenet-Serret curvatures. With the aim of introducing the notation and conventions used in this paper, we first recall the action of a…