Exploration of Dirac equation in H = M^4 x CP_2 Assuming Kahler Structure for M^4

Abstract

The holography = holomorphy vision has led to a dramatic progress in the understanding of Dirac equation in the TGD framework, in particular its variant involving M^4 Kahler form. This article summarizes the latest discoveries. The first topic of this article is Hamilton-Jacobi (H-J) structure, in particular its hyper-complex aspects. The physical implications of M^4 Kahler structure are discussed and the classification of Hamilton-Jacobi structures at the level of H=M^4 x CP_2 and of space-time surfaces are discussed. The main topic of the article are the solutions of H Dirac equation with a non-trivial M^4 Kahler structure.