Related papers: Geometrical particle models on 3D null curves
Physical path integral formulation of motion of particles in Riemannian spaces is outlined and extended to deduce the corresponding field theoretical formulation. For the special case of a zero rest mass particle in Minkowski manifold, it…
In this paper, the parallel transport frames over non-lightlike curves in Minkowski 3-space are introduced. Evolution equations of these frames with respect to arc length and time are calculated over the space of these curves. Then the…
We first describe the numerical invariants attached to the second fundamental form of a spacelike surface in four-dimensional Minkowski space. We then study the configuration of the nu-principal curvature lines on a spacelike surface, when…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
With several concrete examples of zero mean curvature surfaces in $\boldsymbol{R}^3_1$ containing a light-like line recently having been found, here we construct all real analytic germs of zero mean curvature surfaces by applying the…
We show that W_3 is the algebra of symmetries of the ``rigid-particle'', whose action is given by the integrated extrinsic curvature of its world line. This is easily achived by showing that its equation of motion can be written in terms of…
We review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.
We describe how to construct the dynamics of relativistic particles following, either timelike or null curves, by means of an auxiliary variables method instead of the standard theory of deformations for curves. There are interesting…
We study the issue of description of spinning particle dynamics by means of recently proposed world sheet concept. A model of irreducible spinning particle in the $3d$ Minkowski space with two gauge symmetries is considered. The classical…
Spin 1 particle is investigated in 3-dimensional curved space of constant negative curvature. An extended helicity operator is defined and the variables are separated in a tetrad-based 10-dimensional Duffin--Kemmer equation in quasi…
Calabi's Bernstein-type theorem asserts that a zero mean curvature entire graph in Lorentz-Minkowski space $\boldsymbol L^3$ which admits only space-like points is a space-like plane. Using the fluid mechanical duality between minimal…
Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact…
We analyze the possibility of description of D-dimensional massless particles by the Lagrangians linear on world-line curvatures k_i, {\cal S}=\sum_{i=1}^Nc_i\int k_i d{\tilde s}. We show, that the nontrivial classical solutions of this…
In this paper, we study the differential geometry of null Cartan curves under the similarity transformations in the Minkowski space-time. Besides, we extend the fundamental theorem for a null Cartan curve according to a similarity motion.…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
The formulas for the 3-dimensional distance and the velocity modulus in the 4-dimensional linear space with the Berwald-Moor metrics are obtained. The used algorithm is applicable both for the Minkowski space and for the arbitrary…
In this paper, we investigate the similarity transformations in the Minkowski-n space. We study the geometric invariants of non-null curves under the similarity transformations. Besides, we extend the fundamental theorem for a non-null…
Integrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2- and 3- dimensional Minkowski space. The derivation uses a Lorentzian version of a geometrical moving frame method which is known to yield the…
A general action for particles faster than light is presented. It is demonstrated that this action is invariant under reparametrizations. For several cases, it is shown that in the high velocity regime the action is invariant under…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…