Flux quantization and fractional charges of quarks

Two distinct objectives, (A) and (B), characterize this project of flux quantization and particle physics. (A) proposes that, instead of starting with electric point charges to derive magnetic and other properties of (elementary) particles, one may consider spinning, closed loops of quantized flux ${\Phi }_q=\frac{hc}{e}$ as the elementary constituents ("elementary loops") from which electric and other properties of particles are derived. The manifold of alternative forms of one single loop (which follow "fibrations" of ordinary space) represents a lepton. In terms of a heuristic model, the consistency of this program had been shown, and shown to imply the derivation of the electromagnetic coupling constant $\frac{e^2}{\hslash c}$. (B) relates the classification of particles and their conservation laws to the topology of flux loops and of their interlinkage. A magnetic field formed from nonintersecting "loopforms" implies topologically the forms of torus knots. The toroidal fibrations of ordinary three-space by two and three coaxially interlinked quarkloops represent mesons and baryons. The loops may independently spin about their common central symmetry axis and "whirl" about their common circular torus midline; effective spin (versus flux) orientation determines their equivalent electric charges. $\mathfrak{N}$, $\mathcal{P}$, and $\lambda$ quarks correspond to fibrations of space in terms of loops of "winding numbers" (2, 1), (3, 1), and (3, 2), respectively; loops (3, ±2) have "unknotting numbers" ± 1 corresponding to strangeness ± 1. Electromagnetic interactions are, in the conventional way, understood as interactions of distant loops through their electromagnetic field, strong interactions as merging or creation of loop-antiloop pairs, as well as the various different types of exchanges of quark loops between the interacting particles, and weak interactions as crossing of loops over themselves or over those they interact with. This implies that strangeness-violating interactions are weak and parity-violating. The present objective (C) is to consider the existence of the two different types of spin-whirl motion, one of which has the same handedness as that of the fibration, in which case the effective motion of loopforms is subtractively composed of spin and whirl; such was assumed in (B) to characterize quarks. In the other type, i.e., opposite handedness of fibration and of spin-whirl motions, these motions contribute additively to effective motion of torus knots; loops of winding numbers (2, 1) then characterize electrons and muons. The riddle of fractional charges of quarks disappears in this theory. So, also, does the riddle of quark statistics (symmetric spin-isospin functions of baryons) because their linkage makes quark loops localized objects. The flux loops may properly be called "elementary loops." The next objective (D) concerns the probability amplitudes which characterize the distribution of the forms of a torus-knot flux loop. They are shown to be specified by an SO(4)-invariant formulation. To know which group representations to choose from is a prerequisite to a completion of objective (A), and to a quantitative specification of (B).