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 Ec(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.
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BibTeX
@misc{herrmann2026quantum,
title = {{Quantum Field Theory on the Tangent Bundle}},
author = {Joachim Herrmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35778},
eprint = {2610.35778},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35778},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Field Theory on the Tangent Bundle
AU - Joachim Herrmann
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35778
UR - https://arxiv.org/abs/2610.35778
AB - 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.
ER -