After developed the formulation of a "general relativity" in C 4 [?], we proceed with the formulation of a Hamilton-Jacobi equation in C 4 . We argue that in this consideration, the usual problems of the ADM formalism, do not exist, due to the complex time as it exists in our consideration. Specifically, we can derive a suitable dispersion relation in order to work with and find a generalised super Hamiltonian
We explore the possibility to nd the usual quantum theories, within the formulation of a classic theory of mechanics in C4. Specically, by releasing the end-point of the integral 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 Klein-Gordon equation, where the complex functional action S(zi), is identied as the usual complex scalar field φ. Afterwards, we study the energy-momentum 4-d complexvector, in order to re-establish the usual covariant derivative of gauge theories.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.