Related papers: Constrained Dynamics on an Ellipse
We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in $D$ dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first…
The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the antisymmetric part of the…
The ambiguity involved in the definition of effective-mass Hamiltonians for nonrelativistic models is resolved using the Dirac equation. The multistep approximation is extended for relativistic cases allowing the treatment of arbitrary…
The dynamical equations which are basic for the description of the dynamics of quantum felds in arbitrary space--time geometries, can be derived from the requirements of a unique deterministic evolution of the quantum fields, the…
The Dirac equation is used to describe oblique spin-conserving and spin-flip reflections of relativistic electrons from a one-dimensional potential barrier in a vacuum. When an electron hits the barrier from an oblique direction, its…
The distributed system $\mathcal{S}_D$ described by the Dirac equation is investigated simply as a dynamic system, i.e. without usage of quantum principles. The Dirac equation is described in terms of hydrodynamic variables: 4-flux $j^{i}$,…
The unified constrained dynamics is formulated without making use of the Dirac splitting of constraint classes. The strengthened, completely--closed, version of the unified constraint algebra generating equations is given. The fundamental…
We give a geometrical derivation of the Dirac equation by considering a spin-1/2 particle travelling with the speed of light in a cubic spacetime lattice. The mass of the particle acts to flip the multi-component wavefunction at the lattice…
We consider a quantum dot described by a cylindrically symmetric 2D Dirac equation. The potentials representing the quantum dot are taken to be of different types of potential configuration, scalar, vector and pseudo-scalar to enable us to…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
Classical model S{Dcl} of the Dirac particle S_D is constructed. S_D is the dynamic system described by the Dirac equation. For investigation of S_D and construction of S_{Dcl} one uses a new dynamic method: dynamic disquantization. This…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
In this work we produce a classical Lagrangian description of an elementary spinning particle which satisfies Dirac equation when quantized. We call this particle a classical Dirac particle. We analyze in detail the way we arrive to this…
The nilpotent Dirac formalism has been shown, in previous publications, to generate new physical explanations for aspects of particle physics, with the additional possibility of calculating some of the parameters involved in the Standard…
In classical mechanics, external constraints on the dynamical variables can be easily implemented within the Lagrangian formulation. Conversely, the extension of this idea to the quantum realm, which dates back to Dirac, has proven…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…
We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…
Classical mechanical treatment of charged particle beam optics is so far very satisfactory from a practical point of view in applications ranging from electron microscopy to accelerator technology. However, it is desirable to understand the…
For a particle moves on a 2D surface f(x)=0 embedded in 3D Euclidean space, the geometric momentum and potential are simultaneously admissible within the Dirac canonical quantization scheme for constrained motion. In our approach, not the…
In this paper, we show how the motion of physical fields, in particular the electromagnetic potential, is connected with the choice of a space and time decomposition of the background spacetime manifold. The relation of the field dynamics…