From Gradient Postulates to Gauge Structure: Chirality, Conserved Charges, and Constraints on Internal Symmetry
Abstract
We propose a conceptual framework in which, in the non-relativistic static limit, conservative forces arise as gradients of guidance potentials, and the charges that generate these potentials are conserved and form a Lie algebra. We examine what constraints these postulates, together with the empirical facts of parity violation and non-Abelian weak isospin, impose on the internal symmetry group of a gauge theory. We argue that the non-Abelian character of the gauge sector follows from the conserved-charge algebra together with the observed non-Abelian weak isospin algebra. The requirement that the internal group accommodate chiral fermions constrains the admissible representations. Classical stability, charge quantization, and anomaly cancellation provide three physical consistency conditions that strongly constrain the internal group to be compact. With a minimality criterion, the Standard Model group emerges as the minimal candidate among a small set of compact anomaly-free groups with chiral content. We explicitly identify the minimality criterion as a selective assumption rather than a derived result. We do not claim a unique derivation of the Standard Model group. We also show that the scalar guidance potential reproduces Newtonian gravity and Coulomb's law in the non-relativistic limit, and that relativistic consistency requires its upgrade to a metric tensor and gauge vector fields. The postulates substantially constrain the space of viable gauge theories and provide a conceptual basis for treating the gauge group as a constrained rather than arbitrary input.
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BibTeX
@misc{li2026from,
title = {{From Gradient Postulates to Gauge Structure: Chirality, Conserved Charges, and Constraints on Internal Symmetry}},
author = {Xinqiao Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.25336},
eprint = {2607.25336},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.25336},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - From Gradient Postulates to Gauge Structure: Chirality, Conserved Charges, and Constraints on Internal Symmetry
AU - Xinqiao Li
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2607.25336
UR - https://arxiv.org/abs/2607.25336
AB - We propose a conceptual framework in which, in the non-relativistic static limit, conservative forces arise as gradients of guidance potentials, and the charges that generate these potentials are conserved and form a Lie algebra. We examine what constraints these postulates, together with the empirical facts of parity violation and non-Abelian weak isospin, impose on the internal symmetry group of a gauge theory. We argue that the non-Abelian character of the gauge sector follows from the conserved-charge algebra together with the observed non-Abelian weak isospin algebra. The requirement that the internal group accommodate chiral fermions constrains the admissible representations. Classical stability, charge quantization, and anomaly cancellation provide three physical consistency conditions that strongly constrain the internal group to be compact. With a minimality criterion, the Standard Model group emerges as the minimal candidate among a small set of compact anomaly-free groups with chiral content. We explicitly identify the minimality criterion as a selective assumption rather than a derived result. We do not claim a unique derivation of the Standard Model group. We also show that the scalar guidance potential reproduces Newtonian gravity and Coulomb's law in the non-relativistic limit, and that relativistic consistency requires its upgrade to a metric tensor and gauge vector fields. The postulates substantially constrain the space of viable gauge theories and provide a conceptual basis for treating the gauge group as a constrained rather than arbitrary input.
ER -