About the structure of Dirac propagator in TGD

The discussion of the notion of fermion propagator in TGD framework demonstrated that the construction is much more than a mere computational challenge. There are two alternative approaches. Fermionic propagation could correspond to a) a 4-D or lower-dimensional propagation at the space-time level for the induced spinor fields as analog of massless propagation or b) to 8-D propagation in H between points belonging to the space-time surface.

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 M⁴ and CP₂ spinors with fixed M⁴ and CP₂ chiralities whose product is +1 or -1. This suggests that M⁴ 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 CP₂ scale. The M⁴ 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 progator 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 s₁=s₂ is satisfied and implies that the propagation from s₁ is possible to only a discrete set of points s₂. 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. If the condition s₁=s₂ 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.

See the chapter About the structure of Dirac propagator in TGD or the article with the same title.