Related papers: Spinning particles, coadjoint orbits and Hamiltoni…
We examine the structure of the Clifford algebra associated with a Hermitian bilinear form and apply the result to a dynamical model of the relativistic point particle. The dynamics of the particle is described by a Dirac spinor with…
The Hamiltonian formulation of the motion of a spinning relativistic particle in an external electromagnetic field is considered. The approach is based on the introduction of new coordinates and their conjugated momenta to describe the spin…
The relativistic approach to electroweak properties of two-particle composite systems developed previously is generalized here to the case of nonzero spin. This approach is based on the instant form of relativistic Hamiltonian dynamics. A…
The spin-statistics conection is obtained for classical point particles. The connection holds within pseudomechanics, a theory of particle motion that extends classical physics to include anticommuting Grassmann variables, and which…
Starting from the instant form of relativistic quantum dynamics for a system of interacting fields, where amongst the ten generators of the Poincare group only the Hamiltonian and the boost operators carry interactions, we offer an…
In relativistic quantum mechanics, elementary particles are described by irreducible unitary representations of the Poincare group. The same applies to the center-of-mass kinematics of a multi-particle system that is not subject to external…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
We obtain the Poincare group generators by proper choice of arbitrary functions present in the Relativistic Theory of Gravitation (RTG) Hamiltonian. Their Dirac brackets give the Poincare algebra in accordance with the fact that RTG has 10…
The concept of elementary particle rests on the idea that it is a physical system with no excited states, so that all possible kinematical states of the particle are just kinematical modifications of any one of them. The way of describing…
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…
Lagrangian and Hamiltonian formulations of a free spinning particle in 2+1-dimensions or {\it anyon} are established, following closely the analysis of Hanson and Regge. Two viable (and inequivalent) Lagrangians are derived. It is also…
A short review of special relativistic dynamics describing a particle acted upon by an arbitrary conservative external force is presented. If the mass of the particle is zero and the force is central then the equations of motion turn out to…
It is common practice to describe elementary particles by irreducible unitary representations of the Poincar\'e group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincar\'e group.…
In the framework of the generalized Hamiltonian formalism by Dirac, the local symmetries of dynamical systems with first- and second-class constraints are investigated. For theories with an algebra of constraints of special form (to which a…
We discuss a version of Hamiltonian (2+1)-dimensional dynamics, in which one allows nonvanishing Poisson brackets also between the coordinates, and between the momenta. The resulting equations of motion are not any more derivable from a…
The dynamics of a particle moving in background electromagnetic and gravitational fields is revisited from a Lie group cohomological perspective. Physical constants characterising the particle appear as central extension parameters of a…
General relativistic quantum dynamics of twisted (vortex) Dirac particles is constructed. The Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived for a twisted relativistic electron in arbitrary electric…
The relativistic spinning particle model, proposed in [3,4], is analyzed in a Hamiltonian framework. The spin is simulated by extending the configuration space by introducing a light-like four vector degree of freedom. The model is heavily…
A relativistic quantum mechanics is studied for bound hadronic systems in the framework of the Point Form Relativistic Hamiltonian Dynamics. Negative energy states are introduced taking into account the restrictions imposed by a correct…
Although the post-Newtonian Lagrangian formalism is widely used in relativistic dynamical and statistical studies of test bodies moving around arbitrary mass distributions, the corresponding general Hamiltonian formalism is still relatively…