Quantum Field Theory on the Tangent Bundle

Abstract

We develop a quantum-field-theoretical framework on the tangent bundle in which gravitational and internal gauge structures are associated with different sectors of an affine tangent-fiber geometry. The translational sector supplies the coframe and its relation to teleparallel gravity. A reduced vertical spectral problem is based on the centrally extended Euclidean group \(E^{c}(2)\), motivated by projective representations of the stabilizer of a nonzero null vector. Twofold multiplicities of equivalent vertical representations in selected left-chiral sectors admit weak \(SU(2)\) actions, while an assumed threefold quark multiplicity admits a locally gauged color \(SU(3)_c\) symmetry. A proposed global quotient correlates the color center with vertical rotations on a threefold rotation cover. Together with the selected chiral spectrum and anomaly conditions, this construction reproduces the observed fractional quark charge assignments. We formulate matter and gauge-field quantization, BRST symmetry, and anomaly constraints. Under the stated projection assumptions, the color sector has the standard local QCD structure, including its one-loop beta function and asymptotic freedom. Additional gauge bosons and dark-matter states are proposed as hypothetical sectors. We also formulate a structural action for possible couplings between teleparallel torsion and additional Lorentz-sector potentials. The framework relates selected structures of particle physics and gravity within a common geometric setting; their further dynamical and phenomenological development remains open.