Variational principle in post-Riemannian theories of gravitation

On the Variational Principle in the Cartan–Weyl Space

“…On the basis of the gauge theory of the Poincaré-Weyl group it was shown in [1,2] that the Cartan-Weyl space 4 CW is the geometric background in the modern theory of gravitation. In these same works it was shown that within the framework of the gauge procedure the scalar Dirac field  arises in a natural way from geometrical requirements as an important addition to the metric tensor, having as fundamental a geometrical status as the metric tensor itself.…”

“…In the present work we generalize the variational formalism in exterior forms, developed in [3,4] for the Cartan-Weyl space 4 CW , to the presence of the Dirac scalar field, where the additional condition (Q is the Weyl 1-form)…”