New Type of Vector Gauge Theory from Noncommutative Geometry

Using the formalism of noncommutative geometric gauge theory based on the superconnection concept, we construct a new type of vector gauge theory possessing a shift-like symmetry and the usual gauge symmetry. The new shift-like symmetry is due to the matrix derivative of the noncommutative geometric gauge theory, and this gives rise to a mass term for the vector field without introducing the Higgs field. This construction becomes possible by using a constant one form even matrix for the matrix derivative, for which only constant zero form odd matrices have been used so far. The fermionic action in this formalism is also constructed and discussed.Comment: 12 pages, LaTeX file, to appear in Phys. Lett.

Effects of field modulation on Aharonov-Bohm cages in a two-dimensional bipartite periodic lattice

We study the effects of field modulation on the energy spectrum of an electron in a two-dimensional bipartite periodic lattice subject to a magnetic field. Dependence of the energy spectrum on both the period and the strength of field modulation is discussed in detail. Our main finding is that introducing field modulation drastically changes the energy spectrum and the localization properties of the system appearing in the absence of field modulation; the degeneracies induced by a uniform magnetic field are broken and the resultant energy spectrum shows a dispersive band structure, indicating that most of Aharonov-Bohm cages become unbounded. The effects of field modulation on the superconducting transition temperature and the critical current in a wire network with the same geometry are also discussed.Comment: 9 figures; To appear on Phys. Rev. B 62 (15 August, 2000