7,553 research outputs found
An interaction Lagrangian for two spin 1/2 elementary Dirac particles
The kinematical formalism for describing spinning particles developped by the
author is based upon the idea that an elementary particle is a physical system
with no excited states. It can be annihilated by the interaction with its
antiparticle but, if not destroyed, its internal structure can never be
modified. All possible states of the particle are just kinematical
modifications of any one of them. The kinematical state space of the
variational formalism of an elementary particle is necessarily a homogeneous
space of the kinematical group of spacetime symmetries. By assuming Poincare
invariance we have already described a model of a classical spinning particle
which satisfies Dirac's equation when quantized. We have recently shown that
the spacetime symmetry group of this Dirac particle is larger than the Poincare
group. It also contains spacetime dilations and local rotations. In this work
we obtain an interaction Lagrangian for two Dirac particles, which is invariant
under this enlarged spacetime group. It describes a short- and long-range
interaction such that when averaged, to supress the spin content of the
particles, describes the instantaneous Coulomb interaction between them. As an
application, we analyse the interaction between two spinning particles, and
show that it is possible the existence of metastable bound states for two
particles of the same charge, when the spins are parallel and provided some
initial conditions are fulfilled. The possibility of formation of bound pairs
is due to the zitterbewegung spin structure of the particles because when the
spin is neglected, the bound states vanish
The dynamical equation of the spinning electron
We obtain by invariance arguments the relativistic and non-relativistic
invariant dynamical equations of a classical model of a spinning electron. We
apply the formalism to a particular classical model which satisfies Dirac's
equation when quantised. It is shown that the dynamics can be described in
terms of the evolution of the point charge which satisfies a fourth order
differential equation or, alternatively, as a system of second order
differential equations by describing the evolution of both the center of mass
and center of charge of the particle. As an application of the found dynamical
equations, the Coulomb interaction between two spinning electrons is
considered. We find from the classical viewpoint that these spinning electrons
can form bound states under suitable initial conditions. Since the classical
Coulomb interaction of two spinless point electrons does not allow for the
existence of bound states, it is the spin structure that gives rise to new
physical phenomena not described in the spinless case. Perhaps the paper may be
interesting from the mathematical point of view but not from the point of view
of physics.Comment: Latex2e, 14 pages, 5 figure
Order reductions of Lorentz-Dirac-like equations
We discuss the phenomenon of preacceleration in the light of a method of
successive approximations used to construct the physical order reduction of a
large class of singular equations. A simple but illustrative physical example
is analyzed to get more insight into the convergence properties of the method.Comment: 6 pages, LaTeX, IOP macros, no figure
Semiclassical Coherent States propagator
In this work, we derived a semiclassical approximation for the matrix
elements of a quantum propagator in coherent states (CS) basis that avoids
complex trajectories, it only involves real ones. For that propose, we used
the, symplectically invariant, semiclassical Weyl propagator obtained by
performing a stationary phase approximation (SPA) for the path integral in the
Weyl representation. After what, for the transformation to CS representation
SPA is avoided, instead a quadratic expansion of the complex exponent is used.
This procedure also allows to express the semiclassical CS propagator uniquely
in terms of the classical evolution of the initial point, without the need of
any root search typical of Van Vleck Gutzwiller based propagators. For the case
of chaotic Hamiltonian systems, the explicit time dependence of the CS
propagator has been obtained. The comparison with a
\textquotedbl{}realistic\textquotedbl{} chaotic system that derives from a
quadratic Hamiltonian, the cat map, reveals that the expression here derived is
exact up to quadratic Hamiltonian systems.Comment: 13 pages, 2 figure. Accepted for publication in PR
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