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.

Keywords

• Physics beyond the standard model
• Unification of fundamental interactions
• Family problem
• Fractional quark charges