24 research outputs found
Charged Particle with Magnetic Moment in the Aharonov-Bohm Potential
We considered a charged quantum mechanical particle with spin
and gyromagnetic ratio in the field af a magnetic string. Whereas the
interaction of the charge with the string is the well kown Aharonov-Bohm effect
and the contribution of magnetic moment associated with the spin in the case
is known to yield an additional scattering and zero modes (one for each
flux quantum), an anomaly of the magnetic moment (i.e. ) leads to bound
states. We considered two methods for treating the case . \\ The first is
the method of self adjoint extension of the corresponding Hamilton operator. It
yields one bound state as well as additional scattering. In the second we
consider three exactly solvable models for finite flux tubes and take the limit
of shrinking its radius to zero. For finite radius, there are bound
states ( is the number of flux quanta in the tube).\\ For the bound
state energies tend to infinity so that this limit is not physical unless along with . Thereby only for fluxes less than unity the results of
the method of self adjoint extension are reproduced whereas for larger fluxes
bound states exist and we conclude that this method is not applicable.\\ We
discuss the physically interesting case of small but finite radius whereby the
natural scale is given by the anomaly of the magnetic moment of the electron
.Comment: 16 pages, Latex, NTZ-93-0
Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional -function potential case
One-dimensional -function potential is discussed in the framework
of Green's function formalism without invoking perturbation expansion. It is
shown that the energy-dependent Green's function for this case is crucially
dependent on the boundary conditions which are provided by self-adjoint
extension method. The most general Green's function which contains four real
self-adjoint extension parameters is constructed. Also the relation between the
bare coupling constant and self-adjoint extension parameter is derived.Comment: LATEX, 13 page
A pragmatic approach to the problem of the self-adjoint extension of Hamilton operators with the Aharonov-Bohm potential
We consider the problem of self-adjoint extension of Hamilton operators for
charged quantum particles in the pure Aharonov-Bohm potential (infinitely thin
solenoid). We present a pragmatic approach to the problem based on the
orthogonalization of the radial solutions for different quantum numbers. Then
we discuss a model of a scalar particle with a magnetic moment which allows to
explain why the self-adjoint extension contains arbitrary parameters and give a
physical interpretation.Comment: 8 pages, LaTeX, to appear in J. Phys.
Non-Abelian Geometrical Phase for General Three-Dimensional Quantum Systems
Adiabatic geometric phases are studied for arbitrary quantum systems
with a three-dimensional Hilbert space. Necessary and sufficient conditions for
the occurrence of the non-Abelian geometrical phases are obtained without
actually solving the full eigenvalue problem for the instantaneous Hamiltonian.
The parameter space of such systems which has the structure of \xC P^2 is
explicitly constructed. The results of this article are applicable for
arbitrary multipole interaction Hamiltonians and their linear combinations for spin systems. In particular it
is shown that the nuclear quadrupole Hamiltonian does actually
lead to non-Abelian geometric phases for . This system, being bosonic, is
time-reversal-invariant. Therefore it cannot support Abelian adiabatic
geometrical phases.Comment: Plain LaTeX, 17 page
Bremsstrahlung in the gravitational field of a cosmic string
In the framework of QED we investigate the bremsstrahlung process for an
electron passing by a straight static cosmic string. This process is precluded
in empty Minkowski space-time by energy and momentum conservation laws. It
happens in the presence of the cosmic string as a consequence of the conical
structure of space, in spite of the flatness of the metric. The cross section
and emitted electromagnetic energy are computed and analytic expressions are
found for different energies of the incoming electron. The energy interval is
divided in three parts depending on whether the energy is just above electron
rest mass , much larger than , or exceeds , with the
string mass per unit length in Planck units. We compare our results with those
of scalar QED and classical electrodynamics and also with conic pair production
process computed earlier.Comment: 21 pages, to appear in Phys. Rev. D., KONS-RGKU-94-0
Self-Forces on Electric and Magnetic Linear Sources in the Space-Time of a Cosmic String
In this paper we calculate the magnetic and electric self-forces, induced by
the conical structure of a cosmic string space-time, on a long straight wire
which presents either a constant current or a linear charge density. We also
show how these self-forces are related by a Lorentz tranformation and, in this
way, explain what two different inertial observers detect in their respective
frames.Comment: 10 pages, LaTeX, to be published in Phys. Rev. D
Induced vacuum condensates in the background of a singular magnetic vortex in 2+1-dimensional space-time
We show that the vacuum of the quantized massless spinor field in
2+1-dimensional space-time is polarized in the presence of a singular magnetic
vortex. Depending on the choice of the boundary condition at the location of
the vortex, either chiral symmetry or parity is broken; the formation of the
appropriate vacuum condensates is comprehensively studied. In addition, we find
that current, energy and other quantum numbers are induced in the vacuum.Comment: LaTeX2e, 27 page
Euclidean Black Hole Vortices
We argue the existence of solutions of the Euclidean Einstein equations that
correspond to a vortex sitting at the horizon of a black hole. We find the
asymptotic behaviours, at the horizon and at infinity, of vortex solutions for
the gauge and scalar fields in an abelian Higgs model on a Euclidean
Schwarzschild background and interpolate between them by integrating the
equations numerically. Calculating the backreaction shows that the effect of
the vortex is to cut a slice out of the Euclidean Schwarzschild geometry.
Consequences of these solutions for black hole thermodynamics are discussed.Comment: 24 page
Radiative Corrections to the Aharonov-Bohm Scattering
We consider the scattering of relativistic electrons from a thin magnetic
flux tube and perturbatively calculate the order , radiative
correction, to the first order Born approximation. We show also that the second
order Born amplitude vanishes, and obtain a finite inclusive cross section for
the one-body scattering which incorporates soft photon bremsstrahlung effects.
Moreover, we determine the radiatively corrected Aharonov-Bohm potential and,
in particular, verify that an induced magnetic field is generated outside of
the flux tube.Comment: 14 pages, revtex, 3 figure
On the Nonabelian Aharonov Bohm Scattering of Spinless Particles
The Aharonov Bohm scattering for spinless, isospin 1/2, particles interacting
through a nonabelian Chern-Simons field is studied. Starting from the
relativistic quantum field theory and using a Coulomb gauge formulation, the
one loop renormalization program is implemented. Through the introduction of an
intermediary cutoff, separating the regions of high and low integration
momentum, the nonrelativistic limit is derived. The next to leading
relativistic approximation is also determined. In this approach quantum field
theory vacuum polarization effects are automatically incorporated.Comment: 20 pages, 8 figures, revtex. Misspelled reference corrected and new
references adde