Introduction to Quantum Field&nbsp;Theory in <em>C</em>⁴ Space-Time

Abstract

We explore the possibility to nd the usual quantum theories, within the formulation of&amp;nbsp;a classic theory of mechanics in C4. Specically, by releasing the end-point of the integral&amp;nbsp;of the action derived in C4, we derive the dynamic path length of the geodesic equation in C4. In the at case, the derived Hamilton-Jacobi equations, were identied as the usual&amp;nbsp;Klein-Gordon equation, where the complex functional action S(zi), is identied as the&amp;nbsp;usual complex scalar field &amp;phi;. Afterwards, we study the energy-momentum 4-d complexvector, in order to re-establish the usual covariant derivative of gauge theories.

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

“…It is important to simplify a little bit the above mentioned equation by introducing a special case of the embedding functions 1. y α = λδ α x for α = 1, 2, 3 and y 0 = y 0 (x 0 ). As we can see the space-like functions are linear while the time-like function is free and can be (as we can see in our next paper [18]) of the form y 0 = Ae Bx 0 . After some calculus, the metric tensor N ij can be written as…”

“…These energy scales will help us in the third paper of this series [18] to enter in the area of particle physics. Moreover, we must say that before the embedding, C 4 space had an original symmetry (as we shall see in the third paper [18]) which after the embedding has broken into several symmetries. This is exactly what we call in standard model and Higg's mechanism, spontaneous symmetry breaking.…”

“…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.…”

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

“…This is mainly the "road" or way of thinking that we have used in our consideration, in order to derive a bosonic equation in the curved C 4 space, as he wave seen in the third paper [?]. Afterwards, Dirac managed to derive the square root of the Hamiltonian by introducing a new Hamiltonian of first order derivatives in time and space as H = αp + βm (6) where α 2 = β 2 = 1 and {α, β} = 0 and finally has given us the Dirac equation…”