Takesi Saito

Noncommutative quantum mechanics and the Seiberg-Witten map

In order to overcome ambiguity problem on identification of mathematical objects in noncommutative theory with physical observables, quantum mechanical system coupled to the NC U(1) gauge field in the noncommutative space is reformulated by making use of the unitarized Seiberg-Witten map, and applied to the Aharonov-Bohm and Hall effects of the NC U(1) gauge field. Retaining terms only up to linear order in the NC parameter \theta, we find that the AB topological phase and the Hall conductivity have both the same formulas as those of the ordinary commutative space with no \theta-dependence.

Noncommutative Phase Space and the Hall Effect

When phase space coordinates are noncommutative, especially including arbitrarily noncommutative momenta, the Hall effect is reinvestigated. A minimally gauge-invariant coupling of electromagnetic field is introduced by making use of Faddeev-Jackiw formulation for unconstrained and constrained systems. We find that the parameter of noncommutative momenta makes an important contribution to the Hall conductivity.In order to investigate whether phase space coordinates are intrinsically noncommutative, we make use of the Hall effect. A minimally gauge-invariant coupling of an electromagnetic field is introduced, following the Faddeev-Jackiw formulation for constrained and unconstrained systems. We find that noncommutativity parameters in phase space yield an important contribution to the Hall conductivity.

The Gauss-Knörrer map for the Rosochatius dynamical system

Abstract We found a nonlinear integrable system dual to the Rosochatius dynamic system in arbitrary dimensions by means of the Gauss-Knorrer map. The relationship between the Rosochatius system and its dual system is elucidated from the point of view of constrained Hamiltonian systems. Dirac brackets for dynamical variables and conserved quantities for the dual system are derived explicitly.

Left-Right Symmetric Model from Geometric Formulation of Gauge Theory in M4 × Z2 × Z2

The left-right symmetric model (LRSM) with gauge group

Grand Unification from Gauge Theory in M4 ×ZN

SU(2)_{L} \times SU(2)_{R} \times U(1)_{B-L}

A solvable model for fermion masses on a warped 6D world with the extra 2D sphere

is reconstructed from the geometric formulation of gauge theory in

GEOMETRIC FORMULATION OF GAUGE THEORY IN M4×ZN

M_4 \times Z_2 \times Z_2

Parallel transport in gauge theory onM4×Z2geometry

where

N=2 and 4 Super Yang-Mills Theories on M4 ×Z2 ×Z2 Geometry

M_4

Brans-Dicke Theory from M4 ×Z2 Geometry

is the four-dimensional Minkowski space and