arXiv subjects
Publications and source records attributed to K. Ohta.
We construct wave functions and Dirac operator of spin $1/2$ fermions on quantum four-spheres. The construction can be achieved by the q-deformed differential calculus which is manifestly $SO(5)_q$ covariant. We evaluate the engenvalue of the Dirac operator on wave functions of the spinors and show that we can define the chiral fermions in such a way that the massless Dirac operator anti-commutes with $γ_5$.
We report a new solution to explain the observed deficit of the solar neutrino flux by Homestake, Kamiokande II and III, GALLEX and SAGE experiments. We use the matter mixing and the helicity oscillation in the twisting magnetic fields in the sun. Our model predicts the short (seasonal) and long (11 years) time variations of the solar neutrino flux. Three kinds of data observed by Homestake, Kamiokande, GALLEX and SAGE detectors are reproduced well if the mixing angle and the squared mass difference are in the small area around $\sin^2 2θ\simeq 0.01$ and $Δm^2\simeq 1.3\times 10^{-8}{\rm eV}^2$.
We investigate the spin $1/2$ fermions on quantum two spheres. It is shown that the wave functions of fermions and a Dirac Operator on quantum two spheres can be constructed in a manifestly covariant way under the quantum group $SU(2)_q$. The concept of total angular momentum and chirality can be expressed by using $q$-analog of Pauli-matrices and appropriate commutation relations.