On TGD Counterparts of Classical Field Configurations in Maxwell's Theory

Abstract

Classical physics is an exact part of TGD so that the study of extremals of dimensionally reduces 6-D Kahler action can provide a lot of intuition about quantum TGD and see how quantum-classical correspondence is realized. In the following the goal is to develop further understanding about TGD counterparts of the simplest field configurations in Maxwell's theory. In this article  CP₂ type extremals will be considered from the point of view of quantum criticality and the view about string world sheets, their light-like boundaries as carriers of fermion number, and the ends as point like particles as singularities acting as sources for minimal surfaces satisfying non-linear generalization of d'Alembert equation. I will also discuss the delicacies associated with M₄ Kahler structure and its connection with what I call Hamilton-Jacobi structure and with M₈ approach based on classical number fields. I will argue that the breaking of CP symmetry associated with M₄ Kahler structure is small without any additional assumptions: this is in contrast with the earlier view. The difference between TGD and Maxwell's theory and consider the TGD counterparts of simple em field configurations will be also discussed. Topological field quantization provides a geometric view about formation of atoms as bound states based on flux tubes as correlates for binding, and allows to identify space-time correlates for second quantization.  These considerations force to take seriously the possibility that preferred extremals besides being minimal surfaces also possess generalized holomorphy reducing field equations to purely algebraic conditions and that minimal surfaces without this property are not preferred extremals. If so, at microscopic level only CP₂ type extremals, massless extremals, and string like objects and their deformations would exist as preferred extremals and serve as building bricks for the counterparts of Maxwellian field configurations and the counterparts of Maxwellian field configurations such as Coulomb potential would emerge only at the QFT limit.