Physics as Infinite-dimensional Geometry IV: Weak Form of Electric-Magnetic Duality and Its Implications

Abstract

The notion of electric-magnetic duality emerged already two decades ago in the attempts to formulate the Kähler geometry of the "world of classical worlds". Quite recently a considerable step of progress took place in the understanding of this notion. This concept leads to the identification of the physical particles as string like objects defined by magnetic charged wormhole throats connected by magnetic flux tubes. The second end of the string contains particle having electroweak isospin neutralizing that of elementary fermion and the size scale of the string is electro-weak scale would be in question. Hence the screening of electro-weak force takes place via weak confinement. This picture generalizes to magnetic color confinement. Electric-magnetic duality leads also to a detailed understanding of how TGD reduces to almost topological quantum field theory. The condition that the theory reduces to almost topological QFT and the hydrodynamical character of field equations leads to a detailed ansatz for the general solution of field equations and also for the solutions of the modified Dirac equation relying on the notion of Beltrami flow for which the flow parameter associated with the flow lines defined by a conserved current extends to a global coordinate. This makes the theory is in well-defined sense completely integrable. Also Dirac determinant conjectured to represent Kähler function can be calculated explicitly in terms of the geometric data characterizing 3-surfaces.