Chiral Fermions on Quantum Four-Spheres

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 $\gamma_5$.