Do bosons feel spin frames?

In order to allow a coherent dynamicalspinor-matter coupling in a previous paper of ours weintroduced new variables to describe gravitationalfield, related to spin structures and called spinframes. A natural action of spacetime diffeomorphismson spin frames cannot be defined. Accordingly they mustbe treated as a sort of gauge fields, i.e. they must beconsidered to be covariant with respect to automorphisms of some suitable principal bundle. In thispaper we analyze what happens when general bosonicmatter and gauge fields interacting with gravity(described by spin frames) are considered. As should beexpected, such a theory reduces to a theory in whichgravity is described by means of a metric alone.Conserved quantities are also considered indetail.