Related papers: Integrable relativistic systems given by Hamiltoni…
We suggest a numerical integration procedure for solving the equations of motion of certain classical spin systems which preserves the underlying symplectic structure of the phase space. Such symplectic integrators have been successfully…
The general model of an arbitrary spin massive particle in any dimensional space-time is derived on the basis of Kirillov - Kostant - Souriau approach. Keywords: spinning particles, Poincar\'e group, orbit method, constrained dynamics,…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
In parallel to the unified construction of relativistic Hamiltonians based solely on physical arguments [J. Chem. Phys. 160, 084111 (2024)], a unified implementation of relativistic wave function methods is achieved here via programming…
We notice an analogy between the motion of a relativistic particle with external homogeneous and time-dependent electromagnetic fields and the Dik'ii-Eilenberger equation for the Bogoliubov-de Gennes equation. By means of the integrable…
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
In this paper we propose an extended particle model whose evolution is deterministic. In dimension 2, the extended particle is represented by four points that define a small elastic string that vibrates, alternating between a creation…
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behaviour.
We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive…
The coupling of non-relativistic anyons (called exotic particles) to an electromagnetic field is considered. Anomalous coupling is introduced by adding a spin-orbit term to the Lagrangian. Alternatively, one has two Hamiltonian structures,…
We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around a central rotating body by the general relativistic two-body spin-spin and spin-orbit interactions. We use the weak-field…
This work is concerned with suitable choices of tetrad fields and coordinate systems for the Hamiltonian formalism of a spinning particle derived in [E. Barausse, E. Racine, and A. Buonanno, Phys. Rev. D 80, 104025 (2009)]. After…
We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…
We present a non-canonically symplectic integration scheme tailored to numerically computing the post-Newtonian motion of a spinning black-hole binary. Using a splitting approach we combine the flows of orbital and spin contributions. In…
We propose a Hamiltonian for a nonrelativistic spin 1/2 \QTR{it}{free} particle (e.g. an electron) and find that it contains information of its internal degrees of freedom in the rest coordinate system. We comment on the dynamical symmetry…
In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for…
This paper investigates the equations of motion for a relativistic charged particle in a general magnetic field. By reformulating the dynamics in four-dimensional spacetime and separating the linear and nonlinear parts, we construct an…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
In this paper we explore the entanglement of two relativistic spin-$1/2$ particles with continuous momenta. The spin state is described by the Bell state and the momenta are given by Gaussian distributions of product form. Transformations…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the…