Nonassociative Quantum Field Theory: An Introduction

The idea of mathematical beauty in the fundamental equations of nature has driven the unification of various aspects of physics over the last centuries. In this spirit Maxwell’s equations were born and more recently the electroweak unification in the standard model of elementary particle physics. Even with the spectacular success of quantum field theory in the standard model the conceptual difficulties with general relativity and thus understanding the gravitational force at the quantum level are still unsolved. How can these difficulties be overcome? This paper proposes a radically different approach on how to derive the fundamental equations of nature based on a top-down approach,

starting only with a single simple mathematical concept, the Cayley algebra. This compares to the traditional bottom-up approach: Moving from a set of physical model equations derived from experiment up to a more condensed set of equations with the aim to reach a unified view of nature.Following the top-down approach based on a simple field theory over the nonassociative Cayleynumbers leads to mathematical structures that allow a surprisingly tight embedding of particle and interaction concepts found in the standard model of elementary particle physics. But even more important the nonassociative quantum field theory suggests extensions of the standard model to include gravity and puts the problem of quark confinement in a completely new light where it can be seen as pure consequence of the nonassociativity of the theory.