Algebra of Superalgebraic Spinors as Algebra of Second Quantization of Fermions

Abstract

We developed the theory of superalgebraic spinors, which is based on the use of Grassmann densities and derivatives with respect to them in a pseudo- continuous space of momenta. The algebra that they form corresponds to the algebra of second quantization of fermions. We have con-structed a vacuum state vector and have shown that it is symmetric with respect to $P$, $CT$ and $CP T$ transformations. Operators $C$ and $T$ transforms the vacuum into an alternative one. Therefore, time inversion $T$ and charge conjugation $C$ cannot be exact symmetries of the spinors.