Bosons Live in Symplectic Coset Spaces

Abstract

A theory for the transitive action of a group on the configuration space of a system of fermions is shown to lead to the conclusion that bosons can be represented by the action of cosets of the group. By application of the principle to fundamental, indivisible fermions, the symplectic group $Sp(n)$ is shown to be the largest group of isometries of the space. Interactions between particles are represented by the coset space $Sp(n)/ \bigotimes_1^n Sp(1)$.