  It is commonly understood that the Yang-Mills non-Abelian gauge fields is the
natural generalization of the well known Abelian gauge group symmetry $U(1)$ in
the electrodynamics. Taking into account that the problems of the localization
and divergences in QFT are not solved in the framework of the Standard Model
(SM), I proposed a different approach to the quantum theory of the single
self-interacting electron. In connection with this theory, I would like attract
the attention to the state-dependent gauge transformations $U(1) \times U(N-1)$
associated with the Jacobi vector fields of the geodesic variations in the
complex projective Hilbert space $CP(N-1)$ of the unlocated quantum states
(UQS's).
