Computation of the masses of the elementary particles

TL;DR

This paper presents a geometric approach to gauge theory in conformally flat space-time, deriving standard model gauge groups and proposing a method to compute elementary particle masses from the integral mass spectrum, successfully applied to leptons and Z boson.

Contribution

It introduces a geometric framework for gauge theories in conformally flat space-time and a novel mass computation method based on the integral mass spectrum.

Findings

Derived standard model gauge groups from geometry.

Constructed Fock spaces for multiparticle states.

Successfully computed masses for leptons and Z boson.

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 $P_X(G)$ with structure group $G=U(2,2)$. An 11 dimensional bundle $Q$ with structure group a certain 7 dimensional group $K$ is constructed by a method involving a reduction of structure group for the bundle $P_X(G)$. 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, $\mu$ and $\tau$, and the Z$^0$ particle.