Uniform states of the matrix space in a covariant theory of a spinor field

A consistent derivation and analysis is made of all four types of solution corresponding to uniform states of the matrix space introduced by the authors in [1] in constructing a covariant theory of a spinor field. In order to decide which of these types of uniform state is the vacuum state, a study is made of the dynamics of the linear perturbations of the uniform states and it is shown that electron-positron states are contained only in the neighborhood of the Majorana system of Dirac matrices. It follows that the Majorana system describes the vacuum state, of the matrix space. It was precisely the Majorana system of $\gamma$-matrices that was used in [1] in the construction of the linear approximation of the Lagrangian dynamics of the matrix space.