Loop Variables for a Class of Conical Spacetimes

Loop variables are used to describe the presence of topological defects in spacetime. In particular we study the dependence of the holonomy transformation on angular momentum and torsion for a multi-chiral cone. We also compute the holonomies for multiple moving crossed cosmic strings and two plane topological defects-crossed by a cosmic string.Comment: 17 pages, LATE

On the BV structure on the cohomology of moduli space

The question of vanishing of the BV operator on the cohomology of the moduli space of Riemann surfaces is investigated. The BV structure, which comprises a BV operator and an antibracket, is identified, vanishing theorems are proven, and a counterexample is provided

The Jacobi group and the squeezed states - some comments

The generalized coherent states attached to the Jacobi group realize the squeezed states. Imposing hermitian conjugacy to the generators of the Jacobi algebra, we find out the form of the weight function appearing in the scalar product. We show effectively the orthonormality of the base functions with respect to the scalar product. From the explicit form of the reproducing kernel, we find out the expression of the multiplier in a holomorphic representation of the Jacobi group.Comment: 9 pages, to appear in AIP Conference Proceedings, Geometric Methods In Physics, Bialowieza (Poland), June 28 -July 4 2008, Editor(s): P. Kielanowski, S. T. Ali, A. Odzijewicz, M. Schlichenmaier, Th. Vorono

Dirac equation in the magnetic-solenoid field

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann's theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian in both above dimensions and boundary conditions at the AB solenoid. Besides, for the first time, solutions of the Dirac equation in the magnetic-solenoid field with a finite radius solenoid were found. We study the structure of these solutions and their dependence on the behavior of the magnetic field inside the solenoid. Then we exploit the latter solutions to specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm solenoid.Comment: 23 pages, 2 figures, LaTex fil