Conformal extension of gauge theories with spontaneously broken symmetry.

Abstract

By extending O(n) to the conformal group CO(n)=O(n)\ifmmode\times\else\texttimes\fi{}${R}^{+}$ we show that in an O(n) gauge theory with spontaneously broken symmetry the Higgs scalar field may be regarded as a linear approximation of an internal-space conformal factor in a CO(n) covering theory. The conformal factor enters the theory in such a way that it has a natural physical interpretation as a mass field \ensuremath{\Omega}. In the CO(n) theory the masses of the O(n) and ${R}^{+}$ gauge fields depend on the state of the mass field; however, all mass ratios are constant and the O(n) ratios agree with the mass ratios in the standard theory. The \ensuremath{\Omega} field equation reduces to a constraint equation that determines \ensuremath{\Omega} algebraically in terms of the massive gauge fields, and this constraint may be used to eliminate \ensuremath{\Omega} from the Lagrangian. The resulting CO(n) theory describes the usual number of massive and massless O(n) fields together with a new massive gauge-invariant vector field. The gauge fields have quartic self-coupling terms in the Lagrangian, but the masses are now constants. Solutions of the field equations for the CO(n) gauge fields in turn determine the conformal factor \ensuremath{\Omega}, and therefore the massive vector bosons may be viewed as acting so as to produce ``ripples'' in the internal conformal geometry.