Spatial Guidance Field Theory: From Gradient Postulates and Charge Conservation to Gauge Group Structure

Xinqiao Li

high-energy physics phenomenology

Spatial Guidance Field Theory: From Gradient Postulates and Charge Conservation to Gauge Group Structure

arXiv:2607.25336

summary

The paper proposes a unified framework where all fundamental forces arise from gradients of guidance potentials, with conserved charges and chiral fermion requirements forcing the internal symmetry to be a compact non‑Abelian Lie group, uniquely selecting the Standard Model gauge group and yielding predictions for neutron‑star masses and equivalence‑principle violations.

Abstract

We construct a unified framework for interactions from three postulates: (1) all elementary forces arise as gradients of guidance potentials, (2) the charges that generate these potentials are conserved, and (3) the internal symmetry group must accommodate chiral fermions. The chirality postulate forces the internal symmetry group to be non-Abelian. In the non-relativistic limit, a scalar guidance field reproduces Newtonian gravity and Coulomb's law, and relativistic consistency upgrades the potentials to a spacetime metric and gauge vector fields. The central result is a rigorous derivation that the internal symmetry group must be a compact Lie group; combined with anomaly cancellation and minimal rank and representation content, this uniquely selects the Standard Model's $S U (3)_{c} \times S U (2)_{L} \times U (1)_{Y}$ . We present a guidance-field description of strong and weak interactions, and derive coupling-modified Tolman--Oppenheimer--Volkoff equations for neutron stars, obtaining a theoretical maximum mass of $M_{max}^{th} \approx 2.8 \pm 0.4 M_{⊙}$ , naturally accommodating the $2.6 M_{⊙}$ companion of GW190814. We further derive quantitative predictions for equivalence principle violation from nonlinear superposition of guidance potentials, with a QCD-scale benchmark within reach of next-generation experiments. Finally, we discuss implications for black hole interiors within a geometric framework in which charges are topological invariants of a generalized space, and provide the mathematical formulation of the total connection, its action functional, and field equations.

7 pages, 1 tables, this paper has been submitted to JHEP

Topics & keywords

#gauge theory #unified interactions #compact Lie groups #neutron star physics #equivalence principle #guidance potentialsgradient guidance potentialscharge conservationchiral fermionsSU(3)×SU(2)×U(1)anomaly cancellationTolman-Oppenheimer-Volkoff equationsGW190814