Gauge fields arising from spacetime symmetries and gravitational theories. II

The consequences of covariance of the matter Lagrangian under gauge transformations of the second kind of the 15-parameter conformal group are investigated. In order to accomplish this, 44 fields (16 vierbein fields ${h_k}^{\mu }$, 24 rotational gauge fields ${A^{\mathrm{ij}}}_{\mu }$, and 4 scale gauge fields ${\phi }_{\mu }$) are introduced. Furthermore, a Brans-Dicke-type scalar field is used to construct a simple "vacuum" Lagrangian, which is easily reducible to the Einstein Lagrangian; the derived dynamical theory is investigated in the most general case and in various particular cases. Connections are established to many works on this subject. Finally a link is established between the mass of the scalar field and the cosmological constant of Einstein's theory. A possible value is calculated.