Geometrical approach to the gauge field mass problem. Possible reasons for which the Higgs bosons are unobservable.

Abstract

The (4+d)-dimensional Einstein—Hilbert gravity action is considered in the Kaluza - Klein approach. The extra-dimensional manifold V d is a Riemannian space with the d-parametric group of isometries G d which acts on V d by the left shifts and with an arbitrary non-degenerate left-invariant metric ⋗ ab . The gauge fields A μ( x) are introduced as the affine connection coefficients of the fiber bundle with V d being the fiber. The effective Lagrangian L eff{ A μ( x), ⋗ ab } is obtained as an invariant integral of the curvature scalar of the structure considered. The conditions on ⋗ ab are formulated under which L eff{ A μ ( x), ⋗ ab } contains in addition to the square of the gauge field strength tensor also the quadratic form of A μ ( x) and additional fields with pure gauge degrees of freedom. The eigenvalues of the quadratic form are calculated for the case of the gauge group SO(3) and it is shown that they are not equal to zero in the case when ⋗ ab is not proportional to the unit matrix.