Shinsaku Kitakado

On quantum mechanics on compact space

Non-relativistic quantum mechanics is formulated on the surface of a four-dimensional sphere (S3). It is shown that a point particle on S3 can automatically carry spin.

GAUGE STRUCTURE ON SD

Gauge structures, emerging in the course of quantization when the configuration space of the system is SD, are completely determined for arbitrary D. For even D, reflecting the non-trivial topology, the gauge potential is that of the generalized BPST instanton configuration. Similar gauge potentials, although topologically trivial, are obtained for odd D>1.

Induced Gauge Structure for the Zero Modes of Two-Dimensional Solitons

The induced gauge structure for the zero modes of two-dimensional solitons is considered bearing in mind the possibility of finding the origin of gauge fields in field theory.

Vortices as Instantons in Noncommutative Discrete Space: Use of Z(2) Coordinates

We show that vortices of Yang–Mills–Higgs model in R2 space can be regarded as instantons of Yang–Mills model in R2 × Z2 space. For this, we construct the noncommutative Z2 space by explicitly fixing the Z2 coordinates and then show, by using the Z2 coordinates, that BPS equation for the vortices can be considered as a self-dual equation. We also propose the possibility to rewrite the BPS equations for vortices as ADHM equations through the use of self-dual equation.

Negative-Dimensional Group Extrapolation and Dualities in N=1 Supersymmetric Gauge Theories

We point out that the similarities in N=1 supersymmetric SO, SP gauge theories can be explained by using the trick of extrapolating the groups to the negative dimensions. One of the advantages of this trick is that anomaly matching is automatically satisfied. We also give a comment on the problem which one encounters when applying the trick of negative-dimensional group to Spin group duality.

BERRY CONNECTIONS AND INDUCED GAUGE FIELDS IN QUANTUM MECHANICS ON SPHERE

Quantum mechanics on sphere Sn is studied from the viewpoint that the Berrys 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.

INEQUIVALENT QUANTIZATION IN THE SKYRME MODEL

Quantum mechanics on manifolds is not unique, and in general an infinite number of inequivalent quantizations can be considered. These are specified by the induced spin and the induced gauge structures on the manifold. The configuration space of the collective mode in the Skyrme model can be identified with S3 and thus the quantization is not unique. This leads to the different predictions for the physical observables.

The F/D Ratios of Spin-Flip Baryon Vertex in 1/Nc Expansion*>

We calculate the F/D ratios of spin 1/2 baryon vertex for both the non-relativistic quark model and the chiral soliton model with arbitrary number of color degrees of freedom Nc and examine the results in terms of the consistency condition approach for the baryon vertices recently developed by Dashen, Jenkins and Manohar from the viewpoint of QCD. We show that the 1/Nc corrections have two different origins, i.e., one is from the baryon states or baryon wave functions and the other from the vertex operators. Although in the limit Nc->oo the F/D tends to 1/3 in all models, the 1/Nc expansion of F/D ratio does not converge for Nc=3 in the chiral soliton model in contrast to the non-relativistic quark model.