  Modern relativistic theory of the second quantization of fermion and boson
fields is based on the use of the mathematical apparatus of C*-algebras and Lie
superalgebras. In this case, for fermions, the Lorentz transformations are
considered as Bogolyubov transformations of creation and annihilation
operators. However, in this approach one can not obtain an explicit form of the
Dirac gamma-matrices. The mathematical apparatus of the superalgebraic
representation of the algebra of the second quantization of spinors is
developed in the article. It is based on the use of density in the impulse
space of Grassmann variables and their derivatives. It is shown that the Dirac
matrices and the Lorentz transformation generators can be expressed in terms of
such densities. A superalgebraic form of the Dirac equation and the vacuum
state vector are constructed. It is shown that in the superalgebraic form of
the complex Clifford algebra the generators corresponding to the Dirac gamma
matrices are not equivalent. Clifford vector corresponding to diagonal matrix
annihilates the vacuum, and the remaining ones give nonzero values. This means
that there is asymmetric direction corresponding to the time axis
