  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.
