62 research outputs found
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.
Vacuum Polarization of a Charged Massless Scalar Field on Cosmic String Spacetime in the Presence of a Magnetic Field
In this paper we consider a charged massless scalar quantum field operator in
the spacetime of an idealized cosmic string, i.e., an infinitely long, straight
and static cosmic string, which presents a magnetic field confined in a
cylindrical tube of finite radius. Three distinct situations are taking into
account in this analysis: {\it{i)}} a homogeneous field inside the tube,
{\it{ii)}} a magnetic field proportional to and {\it{iii)}} a cylindrical
shell with -function. In these three cases the axis of the infinitely
long tube of radius coincides with the cosmic string. In order to study the
vacuum polarization effects outside the tube, we explicitly calculate the
Euclidean Green function associated with this system for the three above
situations, considering points in the region outside the tube.Comment: 26 pages, LaTex format, 3 figure
Semiclassical gravitational effects near a singular magnetic flux
We consider the backreaction of the vacuum polarization effect for a massive
charged scalar field in the presence of a singular magnetic massless string on
the background metric. Using semiclassical approach, we find the first-order
(in units) metric modifications and the corresponding gravitational
potential and deficit angle. It is shown that, in certain region of values of
coupling constant and magnetic flux, the gravitational potential and deficit
angle can be positive as well as negative over all distances from the string
and can even change its sign. Unlike the case of massless scalar field, the
gravitational corrections were found to have short-range behavior.Comment: 14 pages, 4 figures, journal versio
Fractionalization of angular momentum at finite temperature around a magnetic vortex
Ambiguities in the definition of angular momentum of a quantum-mechanical
particle in the presence of a magnetic vortex are reviewed. We show that the
long-standing problem of the adequate definition is resolved in the framework
of the second-quantized theory at nonzero temperature. Planar relativistic
Fermi gas in the background of a point-like magnetic vortex with arbitrary flux
is considered, and we find thermal averages, quadratic fluctuations, and
correlations of all observables, including angular momentum, in this system.
The kinetic definition of angular momentum is picked out unambiguously by the
requirement of plausible behaviour for the angular momentum fluctuation and its
correlation with fermion number.Comment: 32 pages, submitted to Annals of Physic
Induced quantum numbers of a magnetic vortex at nonzero temperature
The phenomenon of the finite-temperature induced quantum numbers in fermionic
systems with topological defects is analyzed. We consider an ideal gas of
twodimensional relativistic massive electrons in the background of a defect in
the form of a pointlike magnetic vortex with arbitrary flux. This system is
found to acquire, in addition to fermion number, also orbital angular momentum,
spin, and induced magnetic flux, and we determine the functional dependence of
the appropriate thermal averages and correlations on the temperature, the
vortex flux, and the continuous parameter of the boundary condition at the
location of the defect. We find that nonnegativeness of thermal quadratic
fluctuations imposes a restriction on the admissible range of values of the
boundary parameter. The long-standing problem of the adequate definition of
total angular momentum for the system considered is resolved.Comment: 40 pages, 7 figures, journal version, minor correction
Perturbative Study of Bremsstrahlung and Pair-Production by Spin-1/2 Particles in the Aharonov-Bohm Potential
In the presence of an external Aharonov-Bohm potential, we investigate the
two QED processes of the emission of a bremsstrahlung photon by an electron,
and the production of an electron-positron pair by a single photon.
Calculations are carried out using the Born approximation within the framework
of covariant perturbation theory to lowest non-vanishing order in \alpha. The
matrix element for each process is derived, and the corresponding differential
cross-section is calculated. In the non-relativistic limit, the resulting
angular and spectral distributions and some polarization properties are
considered, and compared to results of previous works.Comment: 15 pages, RevTex 4, 2 figures, submitted for publicatio
Fluctuations in the current and energy densities around a magnetic flux carrying cosmic string
We calculate the fluctuations in the current and energy densities for the
case of a quantized, minimally coupled, massless, complex scalar field around a
straight and infinitesimally thin cosmic string carrying magnetic flux. At zero
temperature, we evaluate the fluctuations in the current and energy densities
for arbitrary flux and deficit angle. At a finite temperature, we evaluate the
fluctuations in the energy density for the special case wherein the flux is
absent and the deficit angle equals . We find that, quite generically, the
dimensionless ratio of the variance to the mean-squared values of the current
and energy densities are of order unity which suggests that the fluctuations
around cosmic strings can be considered to be large.Comment: RevTeX, 13 Pages, 3 Figure
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
Polyhedral Cosmic Strings
Quantum field theory is discussed in M\"obius corner kaleidoscopes using the
method of images. The vacuum average of the stress-energy tensor of a free
field is derived and is shown to be a simple sum of straight cosmic string
expressions, the strings running along the edges of the corners. It does not
seem possible to set up a spin-half theory easily.Comment: 15 pages, 4 text figures not include
ДВУМЕРНАЯ МОДЕЛЬ ДЛЯ ОБОСНОВАНИЯ БЕЗОПАСНОСТИ ПУНКТОВ ЗАХОРОНЕНИЯ РАДИОАКТИВНЫХ ОТХОДОВ
Single-dimensional models of contaminants migration in soil do not always adequately reflect the processes that occur in real life. Transition to two- or three- dimensional modeling would help enormously improving accuracy of calculations.Одномерные модели переноса загрязнения в грунте не всегда адекватно отражают реально происходящие процессы. Переход к двумерной или трехмерной моделям позволяет многократно повысить точность расчетов
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