Geometrical Approach to the Gauge Field Mass Problem. Possible Reasons for which the Higgs Bosons Are Not Observable

TL;DR

This paper explores a geometrical approach within Kaluza-Klein theory to understand the gauge field mass problem, suggesting conditions under which gauge fields acquire mass and explaining why Higgs bosons might not be observable.

Contribution

It introduces a generalized principle extending General Relativity to extra dimensions and calculates eigenvalues of gauge field quadratic forms for SO(3), revealing conditions for gauge field masses.

Findings

Eigenvalues of gauge quadratic form are non-zero when g_{ab} is not proportional to the identity.

Effective Lagrangian includes quadratic form of gauge fields, influencing their mass properties.

Conditions on extra-dimensional metrics generalize Einstein's principle to higher dimensions.

Abstract

In the Kaluza - Klein approach the (4+d)-dimensional Einstein--Hilbert gravity action is considered. The extra d-dimensional manifold V_d is a Riemann space with the d-parametric group of isometry $G_d$ which acts on V_d by the left shifts and with arbitrary nondegenerated left-invariant metric g_{ab}. The gauge fields A_{\mu} are introduced as the affine connection coefficients of the fibre bundle with V_d being the fibre. The effective Lagrangian as invariant integral over extra-dimensional manifold of the curvative scalar of mentioned structure is obtained. It is shown that such effective Lagrangian contains beside the square of gauge field strength tensor also quadratic form of A_{\mu} and all other fields have only pure gauge degrees of freedom when g_{ab}. satisfy some conditions. This conditions may be regarded as generalization of the General Relativity Principle to the extra dimensions. The eigenvalues of the quadratic form of A_{\mu} are calculated for the case of gauge group SO(3). It is shown that they are not equal to zero in the case when g_{ab} is not proportional to the unit matrix.