Gravity as a Higgs Field. III. Nongravitional Deviations of Gravitational Fields

Abstract

In Parts I and II of the work (gr-qc/9405013, 9407032), we have shown that gravity is {\it sui generis} a Higgs field corresponding to spontaneous symmetry breaking when the fermion matter admits only the Lorentz subgroup of world symmetries of the geometric arena. From the mathematical viewpoint, the Higgs nature of gravity issues from the fact that different gravitational fields are responsible for nonequivalent representations of cotangent vectors to a world manifold by $γ$-matrices on spinor bundles. It follows that gravitational fields fail to form an affine space modelled on a linear space of deviations of some background field. In other words, even weak gravitational fields do not satisfy the superposition principle and, in particular, can not be quantized by usual methods. At the same time, one can examine superposable deviations $σ$ of a gravitational field $h$ so that $h+σ$ fails to be a gravitational field. These deviations are provided with the adequate mathematical description in the framework of the affine group gauge theory in dislocated manifolds, and their Lagrangian densities differ from the familiar gravitational ones. They make contribution to the standard gravitational effects, e.g., modify Newton's gravitational potential.