Exploration on the Structure of Dirac Propagator in TGD Framework

Abstract

In this article the notion of a fermion propagator in the TGD framework is discussed. It is found that the construction is much more than a mere computational challenge. There are two alternative approaches. Fermionic propagation could correspond a) to 8-D propagation in H between points belonging to the space-time surface or its sub-manifold or b) to a 4-D- or lower-dimensional propagation at the space-time level for the induced spinor fields as analog of massless propagation. For the option a), the separate conservation of baryon and lepton numbers requires fixed H-chirality so that the spinor mode is sum of products of M^4 and CP_2 spinors with fixed M^4 and CP_2 chiralities whose product is +1 or -1. This suggests that M^4 propagation is massless. It came as a total surprise that the propagation of color modes in the conventional sense is not possible in length scales above CP_2 scale. The M^4 part of the propagator for virtual masses above the mass of the color partial wave is of the standard form but for virtual masses below it the propagator is its conformal inversion. The connection with color confinement is highly suggestive. For light-like fermion lines at light-like partonic orbits, there are good reasons to expect that the condition s_1=s_2 is satisfied and implies that the propagation from s_1 is possible to only a discrete set of points s_2. Also this has direct relevance for the understanding of color confinement and more or less implies the intuitively deduced TGD based model for elementary fermions as 1-dimensional geometric objects. Although the option b) need not provide a realistic propagator, it could provide a very useful semiclassical picture for propagation along fermion lines. If the condition s_1=s_2 is assumed, fermionic propagation along light-like geodesics of H is favored and in accordance with the model for elementary particles. This allows a classical space-time picture of particle massivation by p-adic thermodynamics and color confinement. Also the interpretational and technical problems related to the construction of 4-D variants of super-conformal representations having spinor modes as ground states and to the p-adic thermodynamics are discussed.