Introduction to Fermionic Structures&nbsp;in <em>C</em>⁴ Space-Time

Abstract

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

<em>C</em>⁴ Space-Time..&nbsp;A Window to New Physics?

“…This is the first paper of a series of papers [16] [17] [18] [19] [20], concerning a physical theory in an extended C 4 space-time. The most difficult problem in the present history of physics, is the hunt of a unified theory.…”

“…Afterwards, in the fourth paper, complex time will help usto overcome the problems of the ADM formalism and express a suitable Hamilton-Jacobi equation for the curved C 4 , defining this way a super-energy tensorconnected to the complex time. Finally in the fifth paper [20], we introduce 1-linear forms, which could help us to describe fermions pure geometrically.…”

<em>C</em>⁴ Space-Time..&nbsp;A Window to New Physics?

“…This is the first paper of a series of papers [16] [17] [18] [19] [20], concerning a physical theory in an extended C 4 space-time. The most difficult problem in the present history of physics, is the hunt of a unified theory.…”