Origin of Internal Symmetries of the Fundamental Interactions, the Family Problem, Fractional Quark Charges, and Unification in the Tangent Bundle Geometry
Origin of internal symmetries of the fundamental interactions, the family problem, fractional quark charges and unification in the tangent bundle geometry
Abstract
In this letter, we follow the hypothesis that the tangent bundle (TB) with the central extended little groups
of the SO(3, 1)⋊T(1, 3) group as gauge group is the underlying geometric structure for a unified theory of
the fundamental physical interactions. Based on the geometry of the TB, recently, I presented a generalized
theory of electroweak interaction in [1]. The vertical (internal) Laplacian of the tangent bundle possesses
the same form as the Hamiltonian of a 2D semiconductor quantum Hall system. The three families of
leptons and quarks, unlike in the SM, are distinguished by a new quantum number. Here, it will be shown
that the SU(3) color symmetry for strong interaction arises as an emergent symmetry similar to Chern-
Simon gauge symmetries in multicomponent quantum Hall systems and fractional charge quantization of
quarks can be understood by a binding of two vortices to a quark, turning it into a composite quark. The
analogy with the anomalous quantum Hall effect could hint at the possible existence of exotic quark states
with a hypercharge of e/5. Note that based on translational transformations in the TB geometry previously
a gauge theoretical understanding of gravity has been achieved. Therefore, the TB can be considered as the
underlying geometry that could constitute a possible way for the unification of the known fundamental
forces.
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