It is proved that fermions can acquire the mass through the additional
non-integrable exponential factor. For this propose the special vector
potential associated with the spinor field was introduced. Such a vector
potential has close relation with the triality property in Dirac spinors and
plays crucial role in the construction of massive term. It is shown that the
change in phase of a wavefunction round any closed curve with the possibility
of there being singularities in our vector potential will lead to the law of
quantization of physical constants including the mass. The triality properties
of Dirac's spinors are studied and it leads to a double covering vector
representation of Dirac spinor field. It is proved that massive Dirac equation
in the bosonic representation is self-dual.