Towards a unified theory of the fundamental physical interactions based on the underlying geometric structure of the tangent bundle

TL;DR

This paper proposes a geometric framework based on the tangent bundle with extended little groups of SO(3,1) as a gauge group to unify all fundamental interactions, explaining phenomena like fractional charge quantization and quark confinement.

Contribution

It introduces a novel geometric approach using the tangent bundle to unify fundamental interactions and explains emergent symmetries and confinement phenomena.

Findings

Emergent SU(3) color symmetry in the tangent bundle

Explanation of fractional charge quantization of quarks

Prediction of quark confinement as a large-scale Chern-Simons field property

Abstract

This paper pursues the hypothesis that the tangent bundle (TB) with the central extended little groups of the SO(3,1) group as gauge group is the underlying geometric structure for a unified theory of the fundamental physical interactions. Based on this hypothesis as a first step recently I presented a generalized theory of electroweak interaction which includes hypothetical dark matter particles (Eur. Phys. J C 79, 779 (2019). The vertical Laplacian of the tangent bundle possesses the same form as the Hamiltonian of a 2D semiconductor quantum Hall system. This explains fractional charge quantization of quarks and the existence of lepton and quark families. As will be shown the SU(3) colour symmetry for strong interaction arises in the TB as an emergent symmetry similar as Chern-Simon gauge symmetries in quantum Hall systems. This predicts a signature of quark confinement as an universal large-scale property of the Chern-Simon fields and induces a new understanding of the vacuum as the ground state occupied with a condensate of quark-antiquark pairs. The gap for quark-antiquark pairing is calculated in the mean-field approximation which allows a numerical estimation of the characteristic parameters of the vacuum such as its chemical potential, the quark condensation parameter and the vacuum energy. Note that previously a gauge theoretical understanding of gravity has been achieved by considering the translation group T(3,1) in the TB as gauge group. Therefore the theory presented here can be considered as a new type of unified theory for all known fundamental interactions linked with the geometrization program of physics.