New Mixing Angles in the Left-Right Symmetric Model

In the left-right symmetric model neutral gauge fields are characterized by three mixing angles $\theta _{12}, \theta_{23}, \theta_{13}$ between three gauge fields $B_\mu , W^3_{L\mu }, W^3_{R\mu }$, which produce mass eigenstates $A_{\mu }, Z_{\mu }, Z'_{\mu }$, when $G = SU(2)_L\times SU(2)_R\times U(1)_{B-L} \times D$ is spontaneously broken down until $U(1)_{em}$. We find a new mixing angle $\theta '$, which corresponds to the Weinberg angle $\theta _{W}$ in the standard model with the $SU(2)_{L}\times U(1)_{Y}$ gauge symmetry, from these mixing angles. It is then shown that any mixing angle $\theta _{ij}$ can be expressed by $\varepsilon$ and $\theta '$, where $\varepsilon = g_L/g_R$ is a ratio of running left-right gauge coupling strengths. We observe that light gauge bosons are described by $\theta'$ only, whereas heavy gauge bosons are described by two parameters $\varepsilon$ and $\theta '$.Comment: 15 pages, No figure

A Solvable Model for Fermion Masses on a Warped 6D World with the Extra 2D Sphere

In a warped 6D world with an extra 2-dimensional sphere, we propose an exactly solvable model for fermion masses with zero mode. The warp factor is given by $\phi (\theta ,\varphi )=\sin{\theta }\cos{\varphi }$, which is a solution to the 6D Einstein equation with the bulk cosmological constant $\Lambda$ and the energy-momentum tensor of the bulk matter fields. Our model provides another possibility of obtaining fermion zero mode, rather than traditional model based on Dirac's monopole.Comment: 13 pages, no figure. arXiv admin note: substantial text overlap with arXiv:1401.349

Weak gravitation from a small extra 2D sphere

In order to explain weak gravitation in our 4-dimensional universe, a 6-dimensional model with a small extra 2D sphere is proposed. The traceless energy-momentum tensor is quite naturally appeared in our 6-dimensional model. The warp factor is given by $\phi (\theta ) = \epsilon + \sin{\theta }$, where $\epsilon$ plays a role of killing the singular point $\phi (\theta )=0$, and is assumed $0 < \epsilon \ll 1$. Any massive particle is rolling down into points along this geodesic line. The light ray can be shown to stay in our 4-dimensional universe. This suggest us that our 4-dimensional world can be located at $\theta =0$ and/or $\theta = \pi$, its background metric being $\epsilon ^2 \eta _{\mu \nu }$. As a result, we have the 4-dimensional Newton constant, which is given by $G_N \simeq G_6 \epsilon ^{10}$ and the fifth force coefficients appeared here are $\alpha _i\simeq \epsilon ^{2(i-4)}$, $i=1, 2, 3$. Here $G_6$ is the gravitational constant in 6-dimensional spacetime. If we take $\epsilon = 10^{-3.8}$ against $G_6\sim 1($GeV$)^{-2}$, we get $G_N\sim 10^{-38}($Gev$)^{-2}$, the present time gravitational constant.Comment: 16 pages, no figure

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 $\phi (\theta ,\varphi )=\sin{\theta }\cos{\varphi }$, which is a solution to the 6-dimensional Einstein equation with the bulk cosmological constant $\Lambda$ and the energy-momentum tensor of the bulk matter fields.Comment: This paper has been withdrawn by the author due to a crucial error in equation (A11

Noncommutative Hall Effect

When coordinates are noncommutative, the Hall effect is reinvestigated. The Hall conductivity is expressed with noncommutative parameters, so that in the commutative limit it tends to the conventional result.Comment: 7 pages, no figure, uses ptptex.cl

Wigner's Formulation of Noncommutative Quantum Mechanics

When we have noncommutativity among coordinates (or conjugate momenta), we consider Wigner's formulation of quantum mechanics, including a new derivation of path integral formula. We also propose the Moyal star product based on the Dirac bracket in constrained systems.Comment: 10 pages, No figures, Late

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

We consider interactions of a NS open string with first important states of a NS closed string, i.e., a closed-string tachyon and a graviton, where both ends of the NS open string are attached on a D-brane, and a constant background B field is lying along directions parallel to the D-brane world volume. Contrary to general expectations, there are no constraints on these vertex operators coming from the B field. However, we point out that these vertex operators have singularities at both ends of the NS open string when external momenta take some values. These kinds of singularities essentially come from the Dirichlet boundary conditions along directions transverse to the D-brane world volume.Comment: LaTex, 10 pages, no figure

Charged Strings and Spectrum-Generating Algebra

We consider a system that both ends of a charged open string are attached on the D$p$-brane with constant electromagnetic fields. Contrary to neutral strings, the quantization of charged strings has not been so far considered well. For this system we construct the spectrum-generating algebra (SGA), which involves the cyclotron frequency. When the cyclotron frequency is set to be zero, the SGA is reduced to the ordinary SGA for neutral strings. The new SGA for charged strings guarantees that this system is ghost-free if certain conditions are satisfied. We also consider its application to the Hall effect for charged strings.Comment: 12 pages, no figure

A Theoretical Study on Spin-Dependent Transport of "Ferromagnet/Carbon Nanotube Encapsulating Magnetic Atoms/Ferromagnet" Junctions with 4-Valued Conductances

As a novel function of ferromagnet (FM)/spacer/FM junctions, we theoretically investigate multiple-valued (or multi-level) cell property, which is in principle realized by sensing conductances of four states recorded with magnetization configurations of two FMs; (up,up), (up,down), (down,up), (down,down). In order to sense all the states, 4-valued conductances corresponding to the respective states are necessary. We previously proposed that 4-valued conductances are obtained in FM1/spin-polarized spacer (SPS)/FM2 junctions, where FM1 and FM2 have different spin polarizations, and the spacer depends on spin [J. Phys.: Condens. Matter 15, 8797 (2003)]. In this paper, an ideal SPS is considered as a single-wall armchair carbon nanotube encapsulating magnetic atoms, where the nanotube shows on-resonance or off-resonance at the Fermi level according to its length. The magnitude of the obtained 4-valued conductances has an opposite order between the on-resonant nanotube and the off-resonant one, and this property can be understood by considering electronic states of the nanotube. Also, the magnetoresistance ratio between (up,up) and (down,down) can be larger than the conventional one between parallel and anti-parallel configurations.Comment: 10 pages, 4 figures, accepted for publication in J. Phys.: Condens. Matte

Closed Superstrings in a Constant Magnetic Field and Regularization Criterion

We propose a new type of interaction of closed superstrings with the electromagnetic field, other than the usual Kaluza-Klein type or a gauge field with internal gauge group origin. This model with a constant magnetic field is also shown to have an exact solution. We consider a regularization criterion. Some models will be excluded according to this criterion. The spectrum-generating algebra is also constructed in our interacting model.Comment: 22 pages, Nofigure