相关论文: Unfamiliar trajectories for a relativistic particl…
We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
In this note, we first obtain the decomposition of the non-relativistic field velocity into the classical part (i.e., the velocity w=p/m OF the center-of-mass (CM), and the so-called quantum part (i.e., the velocity V of the motion IN the…
Scattering on the ${\cal PT}$-symmetric Coulomb potential is studied along a U-shaped trajectory circumventing the origin in the complex $x$ plane from below. This trajectory reflects ${\cal PT}$ symmetry, sets the appropriate boundary…
The dynamics of relativistic (scalar and vector) bosons through nonminimal vector square (well and barrier) potentials is studied in the Duffin-Kemmer-Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrodinger…
This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross…
Trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations are shown to be classical trajectories. Under convenient conditions, they may exhibit properties typical of chaotic behavior in…
The nonrelativistic Hamiltonians of scalar, spinor and vector particles in the electromagnetic field are studied by applying the Douglas-Kroll-Hess approach. Their relativistic Hamiltonians are expanded on the potential, and the…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
It is shown that Newtonian mechanics is not appropriate to compute approximate individual trajectories with small velocities in chaotic scattering. However, some global properties of the dynamical system, such as the dimension of the…
We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of run-and-tumble particles (RTPs) moving in discrete time on a $d$-dimensional cubic lattice in the presence…
A new approach to quantum gravity is described which joins the loop representation formulation of the canonical theory to the causal set formulation of the path integral. The theory assigns quantum amplitudes to special classes of causal…
The probablity current for a quantum spinless relativistic particle is introduced based on the Hamiltonian dynamics approach utilizing the Salpeter equation as an alternative of the Klein-Gordon equation. The correctness of the presented…
We show that the average trajectories of relativistic quantum particles in Schwarzschild spacetime, obtained via quantum mechanical weak measurements of momentum and energy, are equivalent to the predicted flow lines of probability current…
I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and…
We analyze pure Coulomb high-energy elastic scattering of charged particles (hadrons or nuclei), discarding their strong interactions. We distinguish three scattering modes, determined by the magnitude of the momentum transfer, in which…
Using the relativistic quantum stationary Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding oneself on both relativistic and quantum Lagrangians, we construct a Lagrangian of a relativistic quantum…
We investigate the particle trajectories in an irrotational shallow water flow over a flat bed as periodic waves propagate on the water's free surface. Within the linear water wave theory, we show that there are no closed orbits for the…
A general form of the Hamiltonian for electrons confined to a curved one-dimensional (1D) channel with spin-orbit coupling (SOC) linear in momentum is rederived and is applied to a U-shaped channel. Discretizing the derived continuous 1D…
Models, describing relativistic particles, where Lagrangian densities depend linearly on both the curvature and the torsion of the trajectories, are revisited in D=3 space forms. The moduli spaces of trajectories are completely and…