16 research outputs found
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
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
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
Green functions for generalized point interactions in 1D: A scattering approach
Recently, general point interactions in one dimension has been used to model
a large number of different phenomena in quantum mechanics. Such potentials,
however, requires some sort of regularization to lead to meaningful results.
The usual ways to do so rely on technicalities which may hide important
physical aspects of the problem. In this work we present a new method to
calculate the exact Green functions for general point interactions in 1D. Our
approach differs from previous ones because it is based only on physical
quantities, namely, the scattering coefficients, and , to construct .
Renormalization or particular mathematical prescriptions are not invoked. The
simple formulation of the method makes it easy to extend to more general
contexts, such as for lattices of general point interactions; on a line; on
a half-line; under periodic boundary conditions; and confined in a box.Comment: Revtex, 9 pages, 3 EPS figures. To be published in PR
Zero modes in a system of Aharonov-Bohm fluxes
We study zero modes of two-dimensional Pauli operators with Aharonov--Bohm
fluxes in the case when the solenoids are arranged in periodic structures like
chains or lattices. We also consider perturbations to such periodic systems
which may be infinite and irregular but they are always supposed to be
sufficiently scarce