Bosons Live in Symplectic Coset Spaces

TL;DR

This paper proposes a geometric framework where bosons are represented as cosets of symplectic groups acting on fermionic systems, providing a new perspective on particle interactions in quantum physics.

Contribution

It introduces a novel group-theoretic model linking bosons and fermions through symplectic coset spaces, expanding the understanding of particle symmetries.

Findings

Bosons are represented by cosets of the symplectic group.

The symplectic group $Sp(n)$ is identified as the largest isometry group.

Particle interactions are modeled by specific 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 $Sp(n)/ \bigotimes_1^n Sp(1)$.