Related papers: Symmetries of particle motion
Affine deformations serve as basic examples in the continuum mechanics of deformable 3-dimensional bodies (referred as homogeneous deformations). They preserve parallelism and are often used as an approximation to general deformations.…
The mathematical notion of foliated cobordism is presented, and its relationship to both the motion of extended particles and wave motion is detailed. The fact that wave motion, when represented in such a manner on a four-dimensional…
It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical…
In this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device…
In this paper we consider a manifold with a dynamical vector field and inquire about the possible tangent bundle structures which would turn the starting vector field into a second order one. The analysis is restricted to manifolds which…
The topologically protected transport of colloidal particles on top of magnetic patterns of all possible single lattice constant two dimensional magnetic point group symmetries is studied experimentally, theoretically, and with numerical…
We study numerically the finite temperature and frequency mobility of a particle coupled by a local interaction to a system of spinless fermions in one dimension. We find that when the model is integrable (particle mass equal to the mass of…
The purpose of this paper is to investigate applications the covariant derivatives of the covector fields and killing vector fields with respect to the synectic lift a in a the Riemannian manifold to its tangent bundle, where Cg-complete…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
It is proven that the Poincare symmetry determines equations of motion, which are for massless particles of any spin in d-dimensional spaces linear in the momentum. The proof is made only for even d and for fields with no gauge symmetry. We…
A theory for lifting equations of motion for charged particle dynamics, subject to given electromagnetic like forces, up to a gauge-free system of coupled Hamiltonian Vlasov-Maxwell like equations is given. The theory provides very general…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The…
The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a…
Frames normal for linear connections in vector bundles are defined and studied. In particular, such frames exist at every fixed point and/or along injective path. Inertial frames for gauge fields are introduced and on this ground the…
We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such…
The problem of motion for different test particles, charged and spinning objects of constant spinning tensor in different versions of bimetric theory of gravity is obtained by deriving their corresponding path and path deviation equations,…
Among recently introduced new notions in real algebraic geometry is that of regulous functions. Such functions form a foundation for the development of regulous geometry. Several interesting results on regulous varieties and regulous…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits…