Phase transitions in the early universe can give rise to microscopic topological defects: vacuum domain walls, strings, walls bounded by strings, and monopoles connected by strings. This article reviews the formation, physical properties and the cosmological evolution of various defects. A particular attention is paid to strings and their cosmological consequences, including the string scenario of galaxy formation and possible observational effects of strings.

Cosmic Strings and Domain Walls

In this paper I discuss by means of path integrals the quantum dynamics of a charged particle on the hyperbolic plane under the influence of an Aharonov-Bohm gauge field. The path integral can be solved in terms of an expansion of the homotopy classes of paths. I discuss the interference pattern of scattering by an Aharonov-Bohm gauge field in the flat space limit, yielding a characteristic oscillating behavior in terms of the field strength. In addition, the cases of the isotropic Higgs-oscillator and the Kepler-Coulomb potential on the hyperbolic plane are shortly sketched.

On the Path Integral Treatment for an Aharonov-Bohm Field on the Hyperbolic Plane

In this paper I discuss by means of pathintegrals the quantum dynamics of a charged particle onthe hyperbolic plane under the influence of anAharonov-Bohm gauge field. The path integral can besolved in terms of an expansion of the homotopyclasses of paths. I discuss the interference pattern ofscattering by an Aharonov-Bohm gauge field in theflat-space limit, yielding a characteristic oscillating behavior in terms of the field strength. Inaddition, the cases of the isotropic Higgs oscillatorand the Kepler-Coulomb potential on the hyperbolic planeare briefly sketched.

Path integral treatment of fermions in an Aharonov–Bohm–Coulomb system

Explicit path integration is carried out in a space with a ring-shaped topological defect using toroidal coordinates. The toroidal Aharonov-Bohm experiment is taken as an example.

Path-integral treatment of ring-shaped topological defects

The Green function for a relativistic particle interacting with a gravitational point source and a flux confined at the origin of the ( rho , phi )-space is evaluated using Feynman's summation-over-histories. The bound state energy spectrum is calculated when a uniform magnetic field is applied perpendicular to the ( rho , phi )-space.

C C Bernido

Papers

Path integral treatment of the gravitational anyon in a uniform magnetic field