Akira Kokado

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.

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

In a warped 6-dimensional world with an extra 2-dimensional surface of a sphere, we find a 4-dimensional fermion mass formula with a zero mode. The warp factor is given by

NS Open Strings with B Fields and Their Interactions with NS Closed Strings

\phi (\theta ,\varphi )=\sin{\theta }\cos{\varphi }

Brans-Dicke Theory from M4 ×Z2 Geometry

, which is a solution to the 6-dimensional Einstein equation with the bulk cosmological constant

Closed superstrings in a uniform magnetic field and regularization criterion

\Lambda

Interaction between Noncommutative Open Strings and Closed-String Tachyons

and the energy-momentum tensor of the bulk matter fields.

DYNAMICAL SYMMETRY BREAKING IN A DE SITTER INVARIANT VACUUM

We consider interactions of an NS open string with the first important states of an NS closed string, i.e., a closed-string tachyon and a graviton, where both ends of the NS open string are attached to a D-brane, and a constant background B field lies along directions parallel to the D-brane world volume. Contrary to our expectations, we find that there are no constraints on these vertex operators resulting from the B field. However, we point out that these vertex operators have singularities at both ends of the NS open string when the external momenta take certain values. These kinds of singularities essentially result from the Dirichlet boundary conditions along directions transverse to the D-brane world volume.

Hall effect in noncommutative spaces

The gauge theory on

Constrained Quantization of Charged Strings in a Background B Field and g-Factors

M_4\times Z_2