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

Abstract

We explore the possibility to form a physical theory in C4. We argue that the expansion of our usual 4-d real space-time to a 4-d complex space-time, can serve us to describe geometrically electromagnetism and unify it with gravity, in a different way that Kaluza-Klein theories do. Specially, the electromagnetic eld A&amp;mu;, is included in the free geodesic equation of C4. By embedding our usual 4-d real space-time in the symplectic 8-d real space-time (symplectic R8 is algebraically isomorphic to C4), we derive the usual geodesic equation of a charged particle in gravitational eld, plus new information which is interpreted. Afterwards, we explore the consequences of the formulation of a "special relativity" in the at R8.

<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.…”

“…the first parenthesis in both equations reminds us our usual geodesic equation of the spacetime R 4 , while we have other terms that we want to link them to electromagnetism so that the equations (15), (16) could gives us the geodesic equation of a charged particle in gravitational field and hopefully new elements! It is obvious now, that we want to link the symplectic term I ij (antisymmetric tensor) with a generalised field K µ which will represent a generalised "electromagnetism" which could contain not only the electromagnetic field A µ but the weak nuclear field W µ and the strong nuclear field G µ as well, giving the opportunity to describe those fields purely geometrically in a larger extended space-time.…”