How to present and interpret the Feynman diagrams in this theory describing fermion and boson fields in a unique way, in comparison with the Feynman diagrams so far presented and interpreted?

TL;DR

This paper introduces a novel way to present and interpret Feynman diagrams by using basis vectors in internal spaces that describe fermion and boson fields, providing a unified algebraic framework.

Contribution

It proposes a new interpretation of Feynman diagrams based on basis vectors in internal spaces, linking algebraic multiplication with interactions and offering a unique perspective.

Findings

Algebraic multiplication of basis vectors determines interactions.

Internal space basis vectors can describe fermion and boson states.

Comparison with traditional Feynman diagrams highlights new interpretative insights.

Abstract

Although the internal spaces describing spins and charges of fermions' and bosons' second-quantised fields have such different properties, yet we can all describe them equivalently with the ``basis vectors'' which are a superposition of odd (for fermions) and even (for bosons) products of $\gamma^{a}$'s. In an even-dimensional internal space, as it is $d=(13+1)$, odd ``basis vectors'' appear in $2^{\frac{d}{2}-1}$ families with $2^{\frac{d}{2}-1}$ members each, and have their Hermitian conjugate partners in a separate group, while even ``basis vectors'' appear in two orthogonal groups. Algebraic multiplication of boson and fermion ``basis vectors'' determines the interactions between fermions and bosons, and among bosons themselves, and correspondingly also their action. Tensor products of the ``basis vectors'' and basis in ordinary space-time determine states for fermions and bosons, if bosons obtain in addition the space index $\alpha$. We study properties of massless fermions and bosons with the internal spaces determined by the ``basis vectors'' while assuming that fermions and bosons are active only in $d=(3+1)$ of the ordinary space-time. We discuss the Feynman diagrams in this theory, describing internal spaces of fermion and boson fields with odd and even ``basis vectors'', respectively, in comparison with the Feynman diagrams of the theories so far presented and interpreted.