We propose the two formalisms for obtaining the noncommutative spacetime in a magnetic field. One is the first-order formalism and the other is the second-order formalism. Although the noncommutative spacetime is realized manifestly in the first-order formalism, the second-order formalism would be more useful for calculating the physical quantities in the noncommutative geometry than the first-...

The correlation functions of two-dimensional anyon fields in a KMS-state are studied. The n-particle wave functions of noncanonical fermions of level ν, ν odd, are shown to be of Laughlin type of order ν. For the first noncanonical Fermi class (ν=3) this is simply the finite-temperature generalization of Laughlin wave function. This relates the first and second quantized pictures of the fractio...

We extract the Braid group structure of a recently derived hierarchy scheme for the filling factors proposed by us which related the Hausdorff dimension, h, to the statistics, ν, of the collective excitations in the context of the Fractional Quantum Hall Effect (FQHE).

The traditional Kubo formula is generalized to describe the linear response with respect to non-Abelian fields. To fulfill the demand for studying spin transport, the SU 2 Kubo formula is derived by two conventional approaches with different gauge fixings. Those two approaches are shown to be equivalent where the nonconservation of the SU 2 current plays an essential role in guaranteeing the co...

The spin Hall effect depends crucially on the intrinsic spin-orbit coupling of the energy band. Because of the smaller spin-orbit coupling in silicon, the spin Hall effect is expected to be much reduced. We show that the electric field in p-doped silicon can induce a dissipationless orbital current in a fashion reminiscent of the spin Hall effect. The vertex correction due to impurity scatterin...