Chiral symmetry breaking as a consequence of nontrivial spatial topology

A singular configuration of external static magnetic field in the form of a pointlike vortex polarizes the vacuum of quantized massless spinor field in 2+1-dimensional space-time. This results in an analogue of the Bohm-Aharonov effect: the chiral symmetry breaking condensate, energy density and current emerge in the vacuum even in the case when the spatial region of nonvanishing external field strength is excluded. The dependence of the vacuum characteristics both on the value of the vortex flux and on the choice of the boundary condition at the location of the vortex is determined.Comment: LaTeX2e, 14 page

Charged Particle with Magnetic Moment in the Aharonov-Bohm Potential

We considered a charged quantum mechanical particle with spin ${1\over 2}$ and gyromagnetic ratio $g\ne 2$ 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 $g=2$ is known to yield an additional scattering and zero modes (one for each flux quantum), an anomaly of the magnetic moment (i.e. $g>2$) leads to bound states. We considered two methods for treating the case $g>2$. \\ 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 $N+1$ bound states ($N$ is the number of flux quanta in the tube).\\ For $R\to 0$ the bound state energies tend to infinity so that this limit is not physical unless $g\to 2$ along with $R\to 0$. Thereby only for fluxes less than unity the results of the method of self adjoint extension are reproduced whereas for larger fluxes $N$ 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 $a_e=(g-2)/2\approx 10^{-3}$.Comment: 16 pages, Latex, NTZ-93-0

Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional δ′\delta^{'}-function potential case

One-dimensional $\delta^{'}$-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 $U(2)$ 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 $H=Q^{i_1,\cdots i_n}J_{i_1}\cdots J_{i_n}$ and their linear combinations for spin $j=1$ systems. In particular it is shown that the nuclear quadrupole Hamiltonian $H=Q^{ij}J_iJ_j$ does actually lead to non-Abelian geometric phases for $j=1$. This system, being bosonic, is time-reversal-invariant. Therefore it cannot support Abelian adiabatic geometrical phases.Comment: Plain LaTeX, 17 page

Dirac-like Monopoles in Three Dimensions and Their Possible Influences on the Dynamics of Particles

Dirac-like monopoles are studied in three-dimensional Abelian Maxwell and Maxwell-Chern-Simons models. Their scalar nature is highlighted and discussed through a dimensional reduction of four-dimensional electrodynamics with electric and magnetic sources. Some general properties and similarities of them when are considered in Minkowski or Euclidian space are mentioned. However, by virtue of the structure of the space-time in which they are considered a number of differences among them take place. Furthermore, we pay attention to some consequences of these objects when acting upon usual particles. Among other subjects, special attention is given to the study of a Lorentz-violating non-minimal coupling between neutral fermions and the field generated by a monopole alone. In addition, an analogue of the Aharonov-Casher effect is discussed in this framework.Comment: 20 pages. Latex format. No figures. Accepted for publication in Phys. Rev.

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

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 $M$, much larger than $M$, or exceeds $M/\delta$, with $\delta$ 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

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