Extended form method of antifield-BRST formalism for BF theories

The Batalin-Vilkovisky antifield action for the BF theories is constructed by means of the extended form method. The BRST invariant BV antifield action is directly written down by making use of the extended forms that involve all the required ghosts and antifields.Comment: 8 pages, Shiga-92-

Hopf Map and Quantization on Sphere

Quantization of a system constrained to move on a sphere is considered by taking a square root of the ``on sphere condition''. We arrive at the fibre bundle structure of the Hopf map in the cases of $S^{2}$and $S^{4}$. This leads to more geometrical understanding of monopole and instanton gauge structures that emerge in the course of quantization.Comment: 9 pages, LaTeX2e, uses amsmath.st

Symmetry content of a generalized p-form model of Schwarz-type in d dimensions

We derive the vector supersymmetry and the \L-symmetry transformations for the fields of a generalized topological $p$-form model of Schwarz-type in $d$ space-time dimensions.Comment: 7 page

Inequivalent Quantization in the Skyrme Model

Quantum mechanics on manifolds is not unique and in general infinite number of inequivalent quantizations can be considered. They are specified by the induced spin and the induced gauge structures on the manifold. The configuration space of collective mode in the Skyrme model can be identified with $S^{3}$ and thus the quantization is not unique. This leads to the different predictions for the physical observables.Comment: 16 pages, LaTeX2

Berry Connections and Induced Gauge Fields in Quantum Mechanics on Sphere

Quantum mechanics on sphere $S^{n}$ is studied from the viewpoint that the Berry's connection has to appear as a topological term in the effective action. Furthermore we show that this term is the Chern-Simons term of gauge variables that correspond to the extra degrees of freedom of the enlarged space.Comment: 12 pages, LaTeX2

Runge-Lenz Vector as a 3d Projection of SO(4) Moment Map in R4×R4\mathbb{R}^{4}\times\mathbb{R}^{4} Phase Space

We show, using the methods of geometric algebra, that Runge-Lenz vector in the Kepler problem is a 3-dimensional projection of SO(4) moment map that acts on the phase space of 4-dimensional particle motion. Thus, RL vector is a consequence of geometric symmetry of $\mathbb{R}^4\times \mathbb{R}^4$ phase space