Quaternion Octonion Reformulation of Grand Unified Theories

TL;DR

This paper reformulates Grand Unified Theories using quaternions and octonions, establishing algebraic connections with gauge groups and exploring implications for magnetic monopoles and dyons.

Contribution

It introduces a quaternion and octonion based algebraic framework for GUTs, linking division algebras to gauge groups and fundamental interactions.

Findings

Established connection between division algebras and gauge groups

Re-expressed SU(5) and its subgroups using quaternion and octonion basis elements

Implications for magnetic monopoles and dyons in GUTs

Abstract

In this paper, Grand Unified theories are discussed in terms of quaternions and octonions by using the relation between quaternion basis elements with Pauli matrices and Octonions with Gell Mann \lambda matrices. Connection between the unitary groups of GUTs and the normed division algebra has been established to re-describe the SU(5)gauge group. We have thus described the SU(5)gauge group and its subgroup SU(3)_{C}\times SU(2)_{L}\times U(1) by using quaternion and octonion basis elements. As such the connection between U(1) gauge group and complex number, SU(2) gauge group and quaternions and SU(3) and octonions is established. It is concluded that the division algebra approach to the the theory of unification of fundamental interactions as the case of GUTs leads to the consequences towards the new understanding of these theories which incorporate the existence of magnetic monopole and dyon.