Computation of the masses of the elementary particles

Abstract

An approach to gauge theory in the context of locally conformally flat space–time is described. It is discussed how there are a number of natural principal bundles associated with any given locally conformally flat space–time X. The simplest of these principal bundles is the bundle PX(G) with structure group G = U(2, 2). An 11-dimensional bundle Q with structure group a certain seven-dimensional group K is constructed by a method involving a reduction of structure group for the bundle PX(G). It is shown how the gauge groups U(1), SU(2), and SU(3) can be derived from the geometry of locally conformally flat space–time. Fock spaces of multiparticle states for the fields of the standard model are constructed in the context of bundles with these groups as structure groups. Scattering and other particle interaction processes are defined in terms of linear maps between multiparticle state spaces. A technique for computing analytically and/or computationally the masses of the elementary particles is described. This method involves the computation of a certain quantity called the integral mass spectrum for a given family of particles and then the masses of the particles in the family are determined to be the locations of the peaks of the integral mass spectrum. The method is applied successfully in the electroweak sector to the cases of the charged leptons, μ and τ, and the Z0 particle.