Preprint Article Version 1 This version is not peer-reviewed

Introduction to Fermionic Structures in C4 Space-Time

Version 1 : Received: 17 September 2018 / Approved: 19 September 2018 / Online: 19 September 2018 (08:34:16 CEST)

How to cite: Mastoridis, D.; Kalogirou, K. Introduction to Fermionic Structures in C4 Space-Time. Preprints 2018, 2018090374 (doi: 10.20944/preprints201809.0374.v1). Mastoridis, D.; Kalogirou, K. Introduction to Fermionic Structures in C4 Space-Time. Preprints 2018, 2018090374 (doi: 10.20944/preprints201809.0374.v1).

Abstract

We explore several ways, in order to include fermionic structures naturally in a physical theory in C4. We begin with the standard Dirac formalism and we proceed by using Cartan's property of triality as a second option. Afterwards, we suggest a new approach (in a preliminary basis), by introducing an 1-linear form, as the "square root of the geometry" derived by the usual 2-linear forms (quadratic forms). Keeping this way, we introduce n-linear forms, in order to formulate a new geometric structure, which could be suitable for the formulation of a pure geometric uni ed theory.

Subject Areas

uni ed theories; geometric uni cation; fermionic geometry; Cartan's principle of triality; complex space-time

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