Classification of Multivector Theories and the Modification of the Postulates of Physics

TL;DR

This paper introduces a comprehensive classification of multivector theories in physics, proposing a generalized framework that naturally includes multiple particle generations and extensive gauge fields, potentially guiding new physics research.

Contribution

It presents a novel, unified classification scheme for multivector physics, emphasizing a generalization where wavefunctions are multivectors, enabling more gauge fields and particle generations without larger algebras.

Findings

Multivector wavefunctions naturally include multiple particle generations.

The generalized framework accommodates over ten times more gauge fields.

It offers a unified approach encompassing various existing formulations.

Abstract

We propose a graded classification of the entire field of multivector physics, including all alternative points of view. The (often tacit) postulates of different types of formulations are contrasted, summarizing their consequences. Specifically, spin-gauge formulations of gravitation and GUT which assume standard column spinors will require unnecessarily large matrix algebras. An extreme generalization is introduced, where wavefunctions are multivectors, in which multiple generations of particles naturally appear without resorting to increasing the size of the algebra. Further, this allows for two-sided (bilateral) operators, which can accomodate in excess of 10 times more gauge fields without increasing the algebraic representation. As this generalization encompasses all the essential features of the other categories, it is proposed to be the best path to new physics. [Summary of talk at 3rd International Conf on Clifford Algebras and Their Appl. in Physics, Deinze, Belgium May 1993].