Related papers: First-order differential equations for a particle …
We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite…
First order phase transitions in the early universe naturally lead to the production of a stochastic background of gravitational waves and to the generation of a matter-antimatter asymmetry. The dynamics of the phase transition is affected…
The scientific question resolved by this paper is that the continuity equation appears as an equivalent language of the system of first-order linear ODE. The main result characterizes the fact that the continuity equation contains…
We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We…
In this paper the method of the relativistically-invariant effective tensor representation of Lagrangian decomposition and the amplitudes of the two-photon interaction with hadrons on photon energy is proposed. In the frames…
A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant…
The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 109}, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic…
Emergent Ising$_h^2$ integrability is anticipated in a quantum Ising ladder composed of two weakly-coupled critical transverse field Ising chains. The system is remarkable for including eight types of massive relativistic particles, with…
In this work we study constant-coefficient first order systems of partial differential equations and give necessary and sufficient conditions for those systems to have a well posed Cauchy Problem. In many physical applications, due to the…
The description of particles with spin can be attained by using a spin density matrix in high energy reaction. In this paper we present a parametrization of the spin density matrix for spin -3/2 particles in the Cartesian form. Comparing…
One-dimensional spinor gases with strong delta interaction fermionize and form a spin chain. The spatial degrees of freedom of this atom chain can be described by a mapping to spinless noninteracting fermions and the spin degrees of freedom…
Klein-Gordon and Dirac equations are the motion equations for relativistic particles with spin 0 (so-called scalar particles) and 1/2 (electron/positron) respectively. For a free particle, the Dirac equation is derived from the Klein-Gordon…
First order perturbations for the fields with spin on the background metric of the gravitational shock waves are discussed. Applying the Newman -- Penrose formalism, exact solutions of the perturbation equations are obtained. For particle…
We give a new coherent description of the first-order Fermi acceleration of particles in shock waves from the point of view of stochastic process of the individual particles, under the test particle approximation. The time development of…
A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins),…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
A system consisting of a point material particle and a scalar field described by the nonlinear Klein-Gordon equation has been considered. It has been shown that, when taking into account relativistic effects, in the case of small rest…
We propose in this paper efficient first/second-order time-stepping schemes for the evolutional Navier-Stokes-Nernst-Planck-Poisson equations. The proposed schemes are constructed using an auxiliary variable reformulation and sophisticated…
In this paper, we present new techniques for solving a large variety of partial differential equations. The proposed method reduces the PDEs to first order differential equations known as classical equations such as Bernoulli, Ricatti and…
In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin…